“Our tongue sandwiches speak for themselves” is an old joke about a sign in a deli or restaurant, but such signs actually did exist. “‘Our tongue sandwiches speak for themselves.’—Broadway cafe advertisement” was cited in print in 1906. “Sign in a delicatessen window: ‘Our tongue sandwiches speak for themselves.’—New York American” was cited in 1926.
   
   
Chronicling America
27 November 1906, Los Angeles (CA) Herald, pg. 4, col. 7:
“Our tongue sandwiches speak for themselves.”—Broadway cafe advertisement.
 
31 January 1925, Lebanon (PA) Daily News, pg. 2, col. 7:
Quite Right.
Customer: “How are your tongue sandiwhces?”
Waiter: “Well, sir, they speak for themselves.”
 
12 February 1926, Trenton (NJ) Evening Times, “The Fun Shop” by Maxon Foxhall Judell, pg. 22, col. 1:
TONGUE AND—
Waiter: “A customer wants to know how the tongue sandwiches are.”
Proprietor: “You wil ltell him that the tongue sandwiches speak for themselves.”
—James P. Hughes, Jr.
 
Google News Archive
4 October 1926, Milwaukee (WI) Sentinel, “Stars and Stripes,” pg. 10, col. 2:
Sign in a Third avenue delicatessen: “Our tongue sandwiches speak for themselves.”
 
15 October 1926, Rockford (IL) Republic, pg. 13, col. 8:
Sign in a delicatessen window: “Our tongue sandwiches speak for themselves.”—New York American.
 
Google Books
March 1962, Boys’ Life, “Think and Grin,” pg. 78, col. 2:
Sign in a sandwich shop: “Our tongue sandwiches speak for themselves.” — Chris Siebrasse, Hamilton, Ohio.
   
Google Books
You Don’t Have to Be in Who’s Who to Know What’s What
By Sam Levenson
New York, NY: Simon & Schuster
1979
Pg. 206:
In a delicatessen: OUR TONGUE SANDWICHES SPEAK FOR THEMSELVES
 
Google Books
Smart Alec’s Revolting Jokes for Kids
By Ward Lock, Ward Lock & Co Ltd
New York, NY: Ballantine Books
1989, ©1987
Pg. 37:
Sign in a delicatessen: Our tongue sandwiches speak for themselves.
 
Twitter
Tony Blackburn
‏@tonyblackburn
Sign in a restaurant….Our Tongue sandwiches speak for themselves
4:37 PM - 20 Apr 2013
 
Twitter
Southern With Sass
‏@LilSouthernSass
Signs Of The Times: Restaurant Sign:
“Our tongue sandwiches speak for themselves.”
9:05 PM - 7 Sep 2013