“Smoked salmon should be sliced so thin, you can read the New York Times through it” is an old saying of unknown authorship. “The cucumbers…should be sliced so thin you can read the newspaper through them” was cited in print in 1984 and was said by an anonymous Briton, quoting her grandmother. ‘He slices so thin, you can read the newspaper of your choice through it” was cited in the New York (NY) Times in 2002.
 
“Slices of salmon so thin you can read the paper through them” was said about Manhattan appetizing store Russ & Daughters in 2010. “Thin enough to read a newspaper through it” was said about Russ & Daughters in 2012. “They were slicing smoked salmon; the kind that is sliced so thin you can read the New York Times through it” was said about Russ & Daughters in 2013.
 
 
Google News Archive
6 November 1984, The Spokesman-Review (Spokane, WA), “Custom may fade in England, but tea is thriving in America” by Deborah Leigh Wood (Chicago Tribune), pg. 4F. col 5:
The cucumbers, says the anonymous Briton quoting her grandmother, “should be sliced so thin you can read the newspaper through them.”
 
New York (NY) Times
For Trillin, Parking Is an End, Not a Means
By MEL GUSSOW
Published: February 12, 2002
(...)
After filling the meter, he (Calvin Trillin—ed.) led the way into the store and greeted the owner and his colleague, Herman the Artistic Slicer, who has a magic touch with smoked salmon: ‘‘He slices so thin, you can read the newspaper of your choice through it.’‘
 
Edible Manhattan
Behind the Scenes at Russ & Daughters
By Rachel Wharton March 6, 2010 179 E Houston St New York, NY 10002
(...)
There are many signs on the clean white walls of Russ & Daughters-the Lower East Side landmark that’s been serving smoked sable, pickled herring and slices of salmon so thin you can read the paper through them, since 1914-but the one that tells you all you need to know isn’t the jokey Lox et Veritas (a pun on Yale’s motto of light and truth); or the old-fashioned hand-painted signs that promote “Genuine Sturgeon, Imported Nuts and Caviar”; or even the one reading De gustibus non est disputandum, which is Latin for “of taste there is no dispute” and Russ-ese for “we don’t decide which fish is best, you do.”
     
New York (NY) Times
The Lox Sherpa of Russ & Daughters
By COREY KILGANNON
NOV. 2, 2012
(...)
Most important, they taught him how to cut lox “thin enough to read a newspaper through it,” Mr. Sherpa said.
 
Publishers Weekly
So You Wrote a Book… But Who’s Watching the Register?
Mark Russ Federman talks about his book Russ & Daughters: Reflections and Recipes From the House That Herring Built.
By Marissa Rothkopf Bates | Mar 18, 2013
(...)
They were slicing smoked salmon; the kind that is sliced so thin you can read the New York Times through it.
   
Grub Street
December 6, 2013 9:00 a.m.
Jessica Seinfeld Celebrates Two Thanksgivings, Feasts Late at Charlie Bird
By Alan Sytsma
(...)
We do a run to Zabar’s where two of our favorite guys behind the counter for the past fifteen years, Jerry and David, serve up the best Nova lox in NYC, sliced so thin you can read the New York Times through it.
 
The Huffington Post
Smoked Salmon Infused With Cannabis Is Now A Thing
By Sophie Brown
Posted: 27/05/2015 16:25 BST Updated: 27/05/2015 16:59 BST
(...)
He (Nicky AKA ‘The Fish’ of Rosenbergs Bagels in Denver—ed.) added: “The old saying is that you should slice smoked salmon so thin that you can read it through the New York Times. I guess for this salmon you’d slice it so thin you can read it through the High Times.”