Sabich came to New York City from Israel, where it is popularly served in falafel restaurants. Sabich contains such ingredients as eggplants, fried eggs, hummus, tahini, and amba sauce (an Iraqi mango pickle sauce). A July 26, 2006 New York (NY) Times article described the introduction of sabich to the New York City market in places such as Taim and Chickpea.
 
Sabish is said to have been invented in the 1960s-1970s by Iraqi Jews and it became popular at Ramat Gan (near Tel Aviv). The name “sabich” is said to be an acronym of the Hebrew names for “salad,” “eggs,” and “more eggplant.”
 
 
Wikipedia: Sabich
Sabich (Hebrew: סביח‎) is a food of Middle Eastern origins popular in Israel. It was first brought to Israel by the Iraqi Jews, who used to eat it every Saturday morning. Its name is derived from ‘Sabah’, ‘morning’ in Arabic. One vendor in Ramat Gan claims it originated after his name, and a competing vendor claims Sabich is actually a Hebrew acronym for Salad (סלט), Egg (ביצה), More Eggplant (יותר חציל).
 
Sabich is served as a filling ingredient in a pita bread wrap (i.e. sandwich), containing:
 
peeled fried eggplant
hard-boiled eggs (browned)
Hummus
Tahini
Simple vegetable (tomato and cucumber) salad (Israeli salad)
Amba (condiment) (a mango pickle).
chili sauce (optional)
Minced onion
 
The Israeli city of Ramat Gan is known for having many residents of Iraqi descent and for a long time Sabich was barely known beyond these confines. Today, many falafel stands offer Sabich and some kiosks focus specifically on this dish.
 
Israeli Street Foods
Sabich – the meaning of the word is “morning” in arab, and it is the traditional food Iraqi immigrants introduced to the Israeli street. It may be found on all cities in Israel, mainly in Ramat-Gan. The essence of this food is pita bread with fried eggplants, an egg, salad, tehina and pickles.
   
Google Books
Hebrew Phrasebook
Lonely Planet
1999
Pg. 124:
pita with eggplant sabikh
Pg. 125:
Of Iraqi origin sabikh originated in Ramat Gan almost 30 years ago. Sabikh pita is spread lavishly with hummous, with slices of fried eggplant, and a beitsa Khuma, a “brown egg” (an egg that’s been cooked for a long time). This is topped with a layer of salad, minced onion and tehina, kharif and amba. Delicious!
   
Google Books
The Foods of Israel Today
By Joan Nathan
New York, NY: Knopf
2001
Pg. 92:
This crisp flat loaf, popular throughout Israel as aish tanur, is eaten by Iraqis for all meals, even on the Sabbath, when they eat it for breakfast as sabikh, stuffed with roasted eggplant, a hard-boiled egg, parsley, and tahina.
 
Gems in Israel (October-November 2001)
Sabich - The Alternate Israeli Fast Food
How a Man’s Name Gave Way to a Dish
by Yael Zisling
When you say ‘Israel’ and ‘fast food’ most people instinctively think of falafel. However, there is nothing inherently Israeli about fried chickpea balls. Falafel can be found throughout the Middle East.
 
In recent years a new contender to what has often been considered the national fast food, has become popular, it is Sabich. This dish is also not uniquely Israeli, but rather a traditional dish eaten by Iraqi Jews in the morning, on Shabbat. What exactly is Sabich? It is hummus, fried eggplant, steamed potatoes, (browned) hard-boiled egg, salad and Amba (a mango pickle), all tucked neatly into a pita.
 
Ramat Gan is known for having many residents of Iraqi decent and for a long time Sabich was barely known beyond these confines. That however, has changed. Today, many falafel stands offer Sabich and some kiosks focus specifically on this dish. While you can readily find Sabich, if you want to sample the real thing, visit David “Dudi” Sasson, a second-generation Sabich maker at his kiosk, at 129 Ha’Roeh Street in Ramat Gan.
 
Sasson’s father, Ya’acov Sasson and his partner Zvika Chalavi first started making Sabich at a small kiosk in Ramat Gan’s Uziel Street, in 1958. They later, moved to a new location, also in Ramat Gan.
 
According to Sasson, the dish that was traditionally eaten in Iraq does not have a formal name. When Sasson’s father and his partner established their original kiosk they had to come up with a name for this traditional dish. They decided to simply use one of their own names. That’s how Chalavi’s first name, which is Zvika in Hebrew (and Sabich in Iraqi), became the local name for the dish. Some have asserted that Sabich is actually called Bab Jan in Iraqi, but according to Sasson, Babijan is simply the Iraqi word for eggplant.
 
When I ordered my Sabich without the hard-boiled egg, Sasson was quick to point out that it is exactly the marriage of flavors between hummus and the hard-boiled egg that make the dish unique.
 
In addition to Sabich, Sasson serves Sambusak, an Iraqi version of the classic Indian fritter that is made of an oil-based dough, stuffed with ground chickpeas, fried onions and spices. He notes that the Iraqi version is not as spicy as the Indian version. The Sambusak is something that could easily become addicting. Rounding out the offering is a large selection of syrups, used to make old-fashioned ‘gazoz’ or flavored soda.

Miznon Sabich is located at 129 Ha’Roeh Street, Ramat Gan, between Yehuda Ha’Nassi and Hibbat Zion streets.
 
New York (NY) Times
Passing the Hummus, Reminded of Home
By JAY CHESHES
Published: July 26, 2006
(...)
Start off at Taim, a diminutive falafel-focused spot at 222 Waverly Place (Seventh Avenue South); (212) 691-1287. Taim was among the first to offer the sabich, a pita sandwich of fried eggplant and hard-cooked egg that is as popular in Israel as cheese steaks are in Philadelphia. Traditional condiments for a sabich include pickles, onion, tahini and two types of hot sauce: yellow amba, which is mango based, and red pepper harissa.
 
“In the last five years it’s become a really big sandwich, eaten everywhere,” said Einat Admony, Taim’s chef.
 
The sabich entered the Israeli fast-food pantheon thanks largely to Oved, a one-name-only purveyor in the Tel Aviv suburb of Givatayim. At Oved’s namesake shop, the hot sauce ratios are expressed in soccer score terms using local rivals. For example, Maccabi 2 to Hapoel 1 (Maccabi’s team colors include yellow, Hapoel’s red) would be two parts amba, which is yellow, to one part harissa, which is red. Oved’s shtick helped launch a national sandwich craze.
 
Today, the sabich is making a play in New York. Last year it showed up at Chickpea, 23 Third Avenue (St. Marks Place), with a branch at 210 East 14th Street; (212) 254-9500. The co-owner, Erez Itzhaki, held a contest to give the sandwich a new name.
 
“We wanted to choose a name that would be more friendly,” he said.
 
The result? The Chickplant, which is stuffed into fluffy house-baked pita. Hot sauces come in squeeze bottles.
 
DiscussAnything.com - Let’s eat Sabich!
The face of Jacob
11-19-2006, 01:44 PM
The Sabich is a dish that the Iraqi Jews are eating on Saturday morning.
 
It’s a Pitta with fried eggplants, eggs, humus, vegetables salad and Amba sauce made from Mango.
 
Untill 40 years ago, the sandwiches in Israel were made of cheese and were more or less regular.
 
2 Iraqi Jews decided to open a place which sells Sabich 30-40 years ago in Ramat-Gan which many Jews from Iraq are living in.
 
They were: Yaakov Sasson and Zvi Chalavi. Sabich is also the Iraqi name for the Hebrew name: Zvi (deer) and also the Arabic name for morning: Sabach.
 
In Givatayim (An attached city to Ramat-Gan) there’s a place which sells Sabich in the ownership of Oved Daniel who is from Iraqi descendant.
 
He says that Sabich is the acronym of: Salad, Beitza (egg), Iyoter CHazil (more eggplant). Oved calls his dish in the name of: The best portion in the universe.
(...) (Oved’s soccer nicknames explained in detail—ed.)
You can watch the video of Oved in the middle of this page (http://www.ynet.co.il/articles/0,7340,L-3241709,00.html)

Regarding the other Sabich in Ramat-Gan (http://www.gemsinisrael.com/e_article000039492.htm)
   
My Jewish Learning (2007)
The Inspired Kitchen
Sabich
An Iraqi Jewish classic becomes a new favorite.
By Adeena Sussman
A few years ago, signs began popping up around Tel Aviv and beyond advertising a new delicacy: sabich. This savory combination of fried eggplant, hard-boiled egg, hummus, Israeli salad, and assorted condiments is stuffed into a pita and drizzled with tahini sauce and amba, a mango pickle similar to the chutneys found in Indian cuisine. The dish is now a favorite all over Israel. 
 
But sabich isn’t new to everyone: Iraqi residents, who settled in large numbers in the Tel Aviv suburb of Ramat Gan, brought it (and amba) with them when they immigrated to Israel en masse during the early years of the modern state. There are many theories on the origins of the sandwich’s name. The root letters of sabich—S-B-H—spell “morning” in Arabic, and in fact Iraqi Jews traditionally ate sabich on Sabbath mornings. However, some believe the letters stand for salat, beizah, hazilim (salad, eggs, eggplant)—the sandwich’s main ingredients. Either way, the fusion of textures and flavors—crispy, crunchy, soft, creamy, tangy, and mildly spicy in every bite—is irresistible.
(Long recipe follows—ed.)
 
Food GPS (January 6, 2008)
2007 Top 10 Dishes in Los Angeles
(...)
6. Hummus Bar – Hummus Sabich
Specializing in the Middle Eastern garbanzo bean dip, this spot opened in December 2006 in Tarzana Village, a strip mall in a neighborhood with a large Israeli community. Chef-owner Ziva Ovadia makes everything but the pita fresh daily, including silky, substantial hummus. There are several possible toppings, but none better than with Hummus Sabich ($9.99), roasted eggplant, tahini sauce, thin-sliced hard-boiled egg, parsley and olive oil. The cuts of eggplant were especially terrific, with almost caramelized skins.
 
Flickr
sabich pita
Uploaded on January 6, 2008
by roboppy
 
Taim
Slices of eggplant, fried, layered with an organic hard boiled egg. served with hummus, israeli salad, tahini and amba sauce
 
SO.
FREAKIN’.
AWESOME.
 
And one of the most filling things you could eat. I waddled out of there.
 
Herbvoracious
April 26, 2008
Recipe: Sabich - Iraqi Jewish Eggplant Sandwich
(...)
Sabich - Iraqi Jewish Eggplant Sandwich
Vegetarian; vegan if you omit the egg; gluten free if you omit the pita and serve as a salad
Makes 4 sandwiches
 
4 pieces good pita bread
4 hard boiled eggs (see note above), peeled and sliced
1-2 large eggplants, peeled and sliced 1/4” or so thick
vegetable oil for frying
2 roma tomatoes, finely diced
1/2 English cucumber, finely diced
juice of 1 lemon
hummus (bought or make your own)
prepared tahina (bought or make your own)
1/2 flat leaf parsley
1/2 small white onion minced
1/2 c. pickle, cut into small slices or cubes
amba - mango pickle, or failing that, hot sauce of your choice - harissa maybe?
 
Make a simple salad of the tomatoes, cucumber, and lemon juice, with salt to taste.
Fry the eggplant in batches until thoroughly tender and browned; drain on paper towels and sprinkle with salt.
While the eggplant is frying, put each of the other ingredients in bowls so everyone can build a sandwich to their own specifications.
Toast or grill the pita bread.
Serve it forth, preferably with cold beer, make yourself a gigantic sandwich, and chill.
 
Google Books
Food and Culture
By Pamela Goyan Kittler, Kathryn P. Sucher and Marcia Nelms
Belmont, CA: Cengage Learning
2012
Pg. 415:
European Jews may choose coffeecakes or pancakes, and Middle Eastern Jews may select bureks, kataif (a sweet, stuffed pancake), or sabikh (an Iraqi dish of pita bread topped with fried eggplant, hard-boiled egg, tahini, and a mango pickle)