Garnachas are antojitos (appetizers or snacks) that are almost identical to gorditas.  Garnachas are simply stuffed corn tortillas.
 
“Garnachas” are cited in English from 1888.
 
       
Glossary - Mexican food recipes, cooking terms
Garnachas Another member of the gordita family from the Yucatan, often made with the masa shaped into little “plates” with raised edges, then fried.
 
Mexican Cooking Terminology
Garnachas—stuffed (eg. beef) and fried mini-corn tortillas
       
Wikipedia: Garnacha
Garnacha, “street” foods especially in Mexico. In Oaxaca, it is an actual cuisine: a small corn tortilla fried with shredded meat, cheese, lettuce or a prepared type of cabbage topping. 
 
Gourmet Sleuth
Garnachas Juchitecas
Garnachas are antojitos (appetizers) most typically thick masa cakes topped with a variety of meats, beans, chiles with a sauce and cheese.  The most simple street vendor recipe uses fried wedges of tortillas and tops them with refried beans and cheese. 
 
This recipe is from Diana Kennedy’s My Mexico. The recipe is the regional version from Juchitan.
Makes: 12 - 3” garnachas
I N G R E D I E N T S
The Meat
12 ounces boneless steak, trimmed of fat and cubed
1/2 medium white onion, roughly sliced
2 garlic cloves, coarsely chopped
salt to taste
heaped 1/4 cup finely chopped white onion
 
Garnachas
1 rounded cup masa fresh or prepared for tortillas
1/4 cup (or more) pork lard or oil for frying
1/2 cup (Or more) salsa para garnacha (see recipe)
1/2 cup finely grated queso añejo or Romano
1 heaped cup chilito (see recipe) (...)
   
Google Books
On Horseback:
A Tour in Virginia, North Carolina, and Tennessee
With Notes of Travel in Mexico and California
by Charles Dudley Warner
Boston and New York: Houghton Mifflin and Company
1888
Pg. 226:
At Rinconada, where we met the down train, we (Pg. 227—ed.) stopped an hour for breakfast—a very palatable meal, with Mexican dishes, that are not bad, if you can make up your mind to them, especially the garnachas, compounded of maize, chopped meat, cheese, chiles, tomatoes, and onions.
 
Your Mexican Kitchen:
A Compilation of Mexican Recipes Practicable in the United States
by Natalie V. Scott
New York, NY: G. P. Putnam’s Sons
1935
Pg. 9:
GARNACHAS
Any of the filling suggested for chalupas and quesadillas can be used for garnachas. They are made of the same masa (dough) as tortillas, but are smaller and thicker than the tortillas (see TORTILLAS), about 1/2 to 3/4 of an inch thick, with the edges shaped up like the edge of pie-crust with the fingers, and the center is pinched up, as well.
 
When the filling has been put in, a little hot grease is sprinkled over each one, and it is then put in sizzling hot lard to fry.
   
2 June 1943, Sheboygan (WI) Press, pg. 13, col. 3:
“Garnachas are what we would call in the States hors d’oeuvres.”
   
Google Books
Eating in Mexico
by Amando Farga
Mexican Restaurant Association
1963
Pg. 300:
GARNACHAS—Toasted tortillas, with beans, meat, and chile on top. 
 
Google Books
The Food and Drink of Mexico
by George C. Booth
Los Angeles, CA: Ward Ritchie Press
1964
Pg. 145:
Garnachas con Frijoles Refritos
Garnachas are just the thing to serve the next time your friends come over to watch a football game on TV. Have a reefer full of cold beer, a big platter of garnachas and no one will talk during the close plays.
 
1 doz. tortillas
1 lb. lean beef in chunks
1/2 onion
1/2 green pepper
1 large tomato
Oil
Refried beans (see following recipe)
Powdered yellow cheese
Chopped green onions
Finely chopped lettuce
 
Boil the meat for an hour then put it through a food chopper with the onion, tomato and pepper; sautee until the pepper is tender. Cut the tortillas in quarters and brown in deep fat (commercial corn chips can be used).
 
Spread each one very lightly with refried beans, meat sauce, powdered cheese, chopped onions and lettuce. See next recipe for refried beans. Enough for six nervous football watchers.
 
18 June 1981, Chicago (IL) Daily Herald, section 5, pg. 4, col. 3:
A chef from the La Margarita restaurant on Wabash Avenue will show how to prepare such dishes as garnachas or nachos.
     
8 May 1983, Philadelphia (PA) Inquirer, pg. D1:
Garnachas (tortillas topped with beans, meat, lettuce, tomatoes, onions and cheese) are another appetizing and inexpensive ($2) choice, ... 
   
27 December 1984, Miami (FL) Herald, pg. 4E:
For the trendy, there’s a taco salad in a crisp tortilla bowl ($3.25), Mexican pizza ($4.25) and nachos (known here as garnachas, $2.95) and various ...
     
New York (NY) Times
June 2, 1985
MEXICAN NOTEBOOK
By R. W. APPLE JR.
(...)
Quesadillas (turnovers filled with squash blossoms), garnachas (tortillas spread with beans, vinegar-cured onions and other good things) and gorditas de manteca (tiny tortillas spread with sausage and green sauce) are among the things they do best, but the great specialty is chicken mole in the style of Puebla - the dish that is always hailed as the masterpiece of Mexican cuisine, with its rich sauce of at least 25 ingredients, including hot chilies of several kinds and bitter chocolate.
   
8 May 1988, Chicago (IL) Sun-Times, pg. 14:
On the streets of Oaxaca they are called gorditas (“little fat ones”); In Mexico City they are garnachas.
 
20 May 1988, Dallas (TX) Morning News, “Tacos & Botanas: Leal’s latest a real find”:
Garnachas ($4.15) was a new dish to me—and it was wonderful.
 
5 May 1989, New York (NY) Times, “Diner’s Journal” by Bryan Miller, pg. C20:
Garnachas, which are little tartlets of fried masa filled with shredded chicken, onions, chilies and creme fraiche ($5), are invigorating, too.
   
Google Books
Frommer’s Guide to Mexico on Forty-Five Dollars a Day
by Marita Adair
New York, NY: Macmillan Publishing Company, Incorporated
1994
Garnachas A thickish small circle of fried masa with pinched sides, topped with pork or chicken, onions, and avocado or sometimes chopped potatoes, and tomatoes, typical as a botana in Veracruz and Yucatán. 
 
Google Books
A Cook’s Tour of Mexico
Authentic Recipes from the Country’s Best Open-Air Markets, City Fondas, and Home Kitchens
by Nancy Zaslavsky
New York, NY: St. Martin’s Press
1995
Pg. 308:
Rosario Chavez’s
Garnachas Corn Dough Tartlets Filled with Ground Turkey and Mashed Potatoes
GARNACHAS ARE SMALL MASA TARTLETS layered with seasoned ground turkey and topped with soft mashed potatoes. They are fried in hot oil until golden brown and crisp. The trick is to keep the oil level low and never let it touch the soft potatoes.
   
Try to hunt down these delectable morsels when you’re in Yucatan. They’re known as garnachas or chalupas (don’t confuse them with same-name chalupas found in Puebla and Chiapas); both names are correct and equally used. On rare occasions you’ll see them in fondas at the Valladolid market, but never in Merida. They’re primarily homemade delicacies to have as a light evening meal. While the garnachas are piping hot, with Xnipec (page 302) and/pr Cebolla Curdita (page 304), and a bottle of hot sauce made with habanero chile. (...)
     
Google Groups: houston.eats
Newsgroups: houston.eats
From: “Oscar Caramon”
Date: 1998/09/25
Subject: Re: Weird Things I Love To Eat!
 
- Fried cow guts, with garlic and chili, in soft fried tortillas, called ‘garnachas’. Yummm!
     
Houston (TX) Chronicle
30 April 1999, Houston (TX) Chronicle, “Lo Nuestro serves up basic Guatemalan fare” by Alan Truex, Dining Guide, pg. 8:
Garnachas ($4.25), Guatemala’s version of nachos: Spicy sauteed beef, onions, cheese and tomato sauce top a small circular fried tortilla; the marinated red cabbage salad on the side is a nice bonus.
     
Google Groups: rec.food.cooking
Newsgroups: rec.food.cooking
From: .(JavaScript must be enabled to view this email address) (PENMART10)
Date: 1999/05/23
Subject: Re: Avocado - when to eat & how?
 
I prefer to pan-fry whole tortillas and then break them into manageable pieces by hand - now that’s authentic - that’s how you’ll find them throughout all of Central America where the gringo touristas don’t go.  Whole fried tortillas eaten spread with mashed refried beans, diced tomatillo, fiery hot diced peppers, diced onion, and a bit of grated mild white cheese, they’re called ‘garnachas’, no guacamole.
     
Google Groups: alt.food.mexican-cooking
Newsgroups: alt.food.mexican-cooking
From: “Carlos Bozzo”
Date: 2000/01/22
Subject: Re: Garnachas Poblanas Recipes
 
I found this recipe at the University of Guadalajara.  I have never made it, but you got me curious, so I looked for it.  If you do not understand Spanish, let me know. Enjoy

GARNACHAS POBLANAS
( para 3 personas )
Ingredientes:
15 tortillas, chicas y delgadas
125 grs. de pulpa de cerdo
3 chiles anchos
1/4 taza de cebolla
150 grs. de papas, cocidas y peladas
125 grs. de manteca
sal   (...)
 
Google Groups: alt.food.mexican-cooking
Newsgroups: alt.food.mexican-cooking
From: “Smac”

Date: Mon, 15 Dec 2003 09:12:04 -0600
Local: Mon, Dec 15 2003 10:12 am
Subject: Re: Salbute?
 
“The word antojito comes from the Spanish word antojo, which means whim.”
Antojito is not an entrée or a specific recipe but a (LARGE) category of Mexican dishes (based on tortillas) encompassing:
Burritos, Chimichangas, Enchiladas, Entomatadas, Flautas, Garnachas, Gorditas, Molotes, Panuchos, Papadzules, Pellizcadas, Quesadillas,
Salbutes - “Tortilla masa, often with flour added, is formed into a small, fairly thick tortilla, fried until crisp and light, then topped with shredded meat and vegetables. A specialty of the Yucatan”,
Sopes, Tacos (of all sorts), Tamales, Taquitos, Tlacoyos and Tortas compuestas.