A nice, defining article is "The Egg Cream Mystique" by Wallace Markfield, New York magazine of the Sunday New York Herald Tribune, November 8, 1964, pages 12-13. Five people wrote letters in response (an Auster response is cited, below).
Wikipedia: Egg cream
An egg cream is a classic New York City beverage consisting of chocolate syrup (usually Fox's U-bet chocolate syrup in New York), milk, and seltzer (soda water), probably dating from the late 19th century, and is especially associated with Brooklyn, home of its alleged inventor, candy store owner Louis Auster. It contains neither eggs nor cream.
The egg cream is almost exclusively a fountain drink; although there have been several attempts to bottle it, none have been wholly successful, as its fresh taste and characteristic head requires mixing of the ingredients just before drinking. The drink could be described as a "poor man's ice cream soda," as it has a similar overall flavor, but traditionally sold for only a slight premium over an ordinary fountain soda. Egg creams are sometimes made with other flavors, especially vanilla or strawberry.
The origin of the name "egg cream" is constantly debated. Stanley Auster, the grandson of the inventor, has been quoted as saying that the origins of the name are lost in time. One commonly accepted origin is that Egg is a corruption of the Yiddish word echt ("genuine" or "real") and this was a "good cream". It may also have been called an "Egg Cream" because in the late 1800s, there were already many chocolate fountain/dessert drinks using actual eggs (e.g. 'Egg Brin'), and Auster wanted to capitalize on the name.
(Dictionary of American Regional English)
egg cream n chiefly NYC
A soft drink made with seltzer water, chocolate syrup, and milk.
1964 (1968) Goldman Boys & Girls 62 Chicago IL, He spun into a candy store, ordered an egg cream and downed it in a swallow.
1966 DARE FW Addit NYC, Egg cream -- a soda without ice cream. The soda is made in the normal way, but the scoops of ice cream are not added.
1968 DARE Tape NY118, Egg creams were always big...First of all, there's no eggs and there's no cream in an egg cream whatsoever. It's like chocolate syrup, seltzer and milk, all mixed together, and it's really delicious.
1978 DARE File esWI, [In a conv with owner of Jewish delicatessen:] You can go anywhere in New York City. on Fifth Avenue or the Garment District, where there's a soda fountain, and get an egg cream. There's three categories of soda: for two cents plain, that's seltzer; chocolate phosphate, add chocolate; and egg cream, add milk.
1988 DARE File NYC (as of 1925), A common candy store or luncheonette treat of my childhood was the egg cream, which contained no eggs, but was a combination of chocolate syrup, milk, and seltzer.
Main Entry: egg cream
: a sweetened drink made with milk or cream and other ingredients; especially : a drink consisting of milk, a flavoring syrup, and soda water
(Oxford English Dictionary)
egg cream U.S., any of various kinds of rich sweet drink made orig. with eggs and milk or cream and more recently with milk, soda water, and flavouring.
1841 L. BRYAN Kentucky Housewife 326 *Egg cream. Beat very well the yolks of half a dozen eggs... Make a pint of sweet cream [etc.].
1906 Soda Fountain May 23/1 Egg Drinks... Egg Cream..15c.
1947 I. SHULMAN Amboy Dukes i. 4 The strollers..stood at the open windows of candy stores..drinking..three-cent egg creams.
1975 New Yorker 21 July 22/1 My beloved wife, Whitney, began introducing New York delicacies like borscht, egg creams, and matzohbrei to the populace.
1988 M. STEWART Quick Cook Menus 213 (caption) This chocolate fizz, served in a ruby goblet in front of a leaded window in the hall, is similar to an egg creama traditional New York drink that contains neither egg nor cream.
14 May 1954, Kerrville (TX) Times, pg. 3, col. 3:
The egg cream calls for a shot of cream, vanilla flavor and carbonated water. No egg. And don't ask where the name came from.
(At Oklahoma A&M in Stillwater, OK -- ed.)
3 March 1957, New York (NY) Times, pg. 204:
The first consists of hunting up a neighborhood candy store and ordering an egg cream. An egg cream contains neither eggs nor cream, but is simply a chocolate soda without ice cream (but with milk). A piece of chocolate-covered halvah is eaten with an egg cream and small, nostalgic jokes may be made about how the price has gone up.
20 September 1963, Uniontown (PA) Morning Herald, "It Happened Last Night (in New York)" by Earl Wilson, pg. 4, col. 2:
And when they order an egg cream, they get chocolate syrup, milk, and seltzer -- neither egg nor cream, thus "egg cream."
22 November 1964, New York (NY) Herald Tribune, letter re: "The Egg Cream Mystique" by Wallace Markfield (Nov. 8), "New York" Sunday magazine, pg. 22, col. 2:
To the Editor:
Allow me to enlighten you on a few facts.
We are in business since 1892. We started in at Stanton-Lewis Streets on the lower East Side. About 1900, my father originated egg cream chocolate. We made all our syrups, fresh strawberry, then cherry, pineapple and our finest (and the _world's_ finest) _orange_ syrup. Sodas in those days were 2 cents a 15 oz. glass. or 1 cent you got seltzer with a little syrup on top. Chocolate was 2 cents, and egg cream (pure, cream and eggs, proportioned in a batch of syrup, not an egg to each glass) was 3 cents. There were no pumps to keep syrup in. We used gallon bottles.