Background: The lonely oyster
Evidently, the issue of too much soup from one oyster—or more to the point, not enough oyster for the amount of soup served—has been a focus of criticism by disgruntled diners for more than a century—so much so that the complaint became something of a cliché.
Consider "Brevities," in the [San Francisco] Daily Alta California (December 17, 1873):
A waiter in a cheap restaurant was asked for a toothpick by one of the patrons—he had just finished a bowl of oyster soup. "What do you want with a toothpick?" queried the waiter, who had cultivated considerable familiarity with all the customers. "I want to pick an oyster from my teeth." "Oh, no you don't! There was only one oyster in that soup, and I ate that on my way from the kitchen!"
From "New Improvements in Bivalves," in Illustrated Science News (December 15, 1878, reprinted from the [Louisville, Kentucky] Courier-Journal of November 25, 1878):
In partaking of oyster soup in hotels in the West, a feeling of awe has often crept over me when I contemplated the solitary oyster that generally reposed in the centre of my plate, surrounded, as it were, by an ocean. What, I thought, must be its feelings (if it has feelings) to find itself so isolated? But neither the hotel proprietor nor any of his employes should be blamed for the situation. I have lately ascertained the reason why there is only one oyster in each plate of soup served up in hotels in the West.
I am informed by a friend who has just returned from the East, and who, while there, thoroughly examined the principal industries of New England, that a Connecticut company had been formed, and were doing very successful business supplying the Western and Southern markets with gum-arabic oysters.
From an untitled item in the [Pueblo, Colorado] Chieftain (September 23, 1882):
Time is drawing near for the churches to give oyster suppers, and in this connection it is proper to remark that we never did understand how one oyster could wade through three or four hundred dishes of soup and survive the trying ordeal.
From "Welcome Address: Delivered by Freeman E. Miller to the Panhandle Press Association, at Canadian, February 22, 1888; Published by Its Request," in the Canadian [Texas] Crescent (March 2, 1888):
His [the editor's] joys are few and far between, being mainly an empty purse and a character unspotted from the world. Because he sits with great men at political gatherings and goes free to the circus and the slight-of hand show, he is called a dead-head of the first water. Because he advertises $500 worth in a year for a soulless corporation and rides out $10 of it on a "free pass," he is looked upon as an incumbrance by railroad conductors. He may be invited to church festivals and be given a pint of soup, made by hanging one oyster for two hours over a barrel of water with a two inch rope, in return for half a column of puffs.
From "Same Thing," in the [Stanford, Kentucky] Semi-Weekly Interior Journal (June 2, 1891):
Customer (to waiter)—I'd like some crackers and a bowl of milk. Have the milk hot.
Waiter (giving the order)—One oyster stew!—Harper's Bazar.
From "Breezy Bits," in the Salt Lake [City, Utah] Herald (May 13, 1895):
Miss Curiosity—It true, deacon, that one oyster served for the stew at the parish supper?
Deacon—A whole oyster for that stew? For mercy's sake, what are you thinking of?—Boston Transcript
From "The Crier Announces Court," in the Cambridge [Massachusetts] Chronicle (February 12, 1898):
Oliver H. Durrell was charged with eating all the oysters in a stew at a church festival. His attorney moved to quash, the indictment being defective. "It says 'oysters,'" argued the learned man of the law, "and not more than one oyster has ever been found in a church stew in Cambridge." That settled the point, and nothing more was said in that case.
From an untitled item in the Saint Paul [Minnesota] Globe (March 22, 1898):
Klondike parties are becoming popular in church societies. The Klondike consists of selling soup, made of one oyster and a gallon of water, at 25 cents a dish.
From Jessup Whitehead, The Hotel Fish and Oyster Cook (1901):
Now, at last, it is the cook's turn to talk back about that hotel oyster soup that they say has only one oyster, which, of course, is no such thing. Some of the guests get a whole plateful of oysters, particularly if the waiters are girls and allowed to help themselves to the tureen. Why, anyway, does the man who gets only one oyster come so late?
From an untitled item in the Yuma [Colorado] Pioneer (November 14, 1902):
The oyster supper next Tuesday night will be something different from the ordinary church oyster supper, for the ladies have promised to give more oysters to the soup than the old-time allotment of "one oyster"—the miserable, lonesome oyster passed from one church to the other to help swell the fund and keep the soup in good spirits.
From "What Shall Be the Attitude of the Sunday-Schools of Our Conference Towards the Festival?" in the [New Market, Virginia] Our Church Paper (July 5, 1904):
There is most always irreverence and often dishonesty connected with these festivals. They are looked upon as a part of the exercises of the church, they are wholly devoid of any aspect of reverence, and are calculated to beget and foster irreverence of all sacred things. True Christian giving is an act of worship and should be done with reverence and not with levity. I can not of my own knowledge testify to any dishonesty practiced, but the oyster stew with one oyster of the church festival, has become proverbial among non-church people. Little deceptions are often practiced in order to make a dime, and cakes and other things are gambled for and chanced off.
From The New Pun Book: Collected, Edited and Arranged from the Notes of Two Learned Pundits (1906):
"I had soup in a restaurant the other day and found an oyster in it."
"Great Scott! That one oyster in the soup joke is old."
"Yes, but this was tomato soup."
From an untitled item in the Chicago [Illinois] Livestock World (January 9, 1908):
Modern society is nothing but hypocrisy and sham, according to Prof. Zueblin. The professor must have been attending a church social where there was only one oyster to a barrel of oyster stew.
From Samuel Hudson, Pennsylvania and Its Public Men (1909):
"Now, I was about to remark that it don't pay the political workers of a ward to capture a row officer for their diocese. After they have succeeded what else do they get? Why, soup. Yes, my esteemed friend, and infernally thin soup at that. You have seen oyster soup embracing one oyster—one little, lonely, emasculated tariff reform oyster. You have doubtless seen bean soup with one disconsolate puritanical New England bean in it. You have tasted erstwhile chicken soup with the chicken thrown into it by the aid of a camera obscura. Well, that is the type of soup a ward falls heir to after it has captured a row office. ..."
And from "Nothing Serious," in the [Chicago, Illinois] Saturday Blade (April 23, 1911):
Two oysters were in a big pot full of milk, getting ready for stew. Said one oyster to the other: “Where are we?” “In a church supper,” was the reply. Whereupon the little oyster said: “What on earth do they want of both of us?”
It seems very likely that the one-oyster restaurant soup or the one-oyster church festival stew—which the sober (and indeed humorless) author of the Our Church Newspaper characterizes in 1904 as "proverbial among non-church people—is the progenitor of the expression that you ask about. Certainly allusions to it have been a familiar phenomenon for more than 140 years.
The idiom/expression/catch-phrase itself
As for the idiom or expression or catch-phrase itself, a version of it appears as the caption of a political cartoon in the Urbana [Illinois] Daily Courier March 20, 1928), in which an old woman (labeled "Miss Democracy") dips an oyster (labeled "The 1920 Oil Scandal Oyster") into a series of boiling stew pots, which are then carried of to serve a crowd of people seated beneath a sign reading "Democratic Picnic":
Did You Ever See So Much Stew From One Oyster?
A very similar phrase appears as an article headline in Public Utilities Fortnightly (1937) [snippet view]:
DID YOU EVER SEE ANYONE MAKE SO MUCH SOUP FROM ONE OYSTER?
Another appears as a cartoon caption in Review of Reviews and World's Work (1932), reprinted from the Philadelphia [Pennsylvania] Inquirer [snippet view, with almost none of the cartoon visible]:
WHAT A LOT OF SOUP FROM ONE OYSTER
A different political cartoon in the San Bernardino [California] Sun (May 8, 1932) shows a goofy-looking cook (labeled "Our Cock-Eyed Congress") dipping an oyster (labeled "U.S. Dollar" into a succession of boiling cauldrons, the last of which is labeled "Inflated U.S. Currency Soup." The cartoon's caption reads as follows:
How Much Soup Can You Make With One Oyster?
That your family is not alone in using the idiom today is evident from this recent posting on the Thunderbolts Forum, dated November 21, 2017:
Not all plasma discharges reach "glow mode." There are "asteroid" belt objects with orbits eccentric enough to form comas, yet those orbits are hardly "cometary." Why are they visible?
Rendezvous with Rama? Some have suggested the object might be an alien spacecraft. As with most mainstream astronomy, it's an awful lot of chowder from one oyster—like the alien megastructure around KIC 8462852.
The expression isn't common today, but it has been around for at least ninety years. To judge from the matches that my database searches uncovered, it seems to have been most popular as a figurative phrase during the period from 1928 through 1937.