A round burger (such as a hamburger or a turkey burger or a veggie burger) can resemble a hockey puck. A burger cooked “well done” is often blackened and tough as a hockey puck to eat.
 
“Well-done hockey puck” was used to describe a hamburger eaten by Florence Fabricant of the New York (NY) Times in 1976. 
 
 
Wikipedia: Diner lingo
Hockey puck: a hamburger, well done
 
Urban Dictionary
hockey puck
A real shity hamburger,
you know… the kind they serve in the school lunch room.
I’m not eating in the cafeteria , they are servin’ hockey pucks today.
by mavros Apr 24, 2006
 
5 December 1976, New York (NY) Times, “Eating on the Turnpike” by Florence Fabricant, pg. 389:
The chopped steak had acceptable flavor, and while the texture was somewhat compressed, characteristic of a machine-formed patty, it was infinitely preferable to the Holiday House version that first emerged like a large, well-done hockey puck and on a second try was medium-rare, all right, but cold in the middle.
     
5 April 1985, New York (NY) Times, “Books of The Times” by John Gross, pg. C25: 
As always with Mr. De Vries, virtually every page of “The Prick of Noon” is enlivened by a happy invention. Images linger—the hamburger that looks like “a hockey puck on a bun” or the new pair of shoes that meow.
 
Google Books
Dictionary of Popular Slang
By Anita Pearl
Middle Village, NY: Jonathan David Publishers
1990
Pg. 90:
hockey puck n. a hamburger.
 
20 February 1992, Chicago (IL) Daily Herald sec. 6, pg. 5, col. 2:
You can only go so far de-fatting beef before it tastes unpalatable. Even as it is, says May of the USDA, cooks must cut their cooking times. Anyone who cooks the newer beef too long will chew on a hockey puck, he says; whereas with well-marbled beef, “you can cremate it and still eat it.”
   
Google Books
New York Eats (More)
By Ed Levine
New York, NY: St. Martin’s Griffin
1997
Pg. 291:
The tuna burger is an oversized hockey puck made with nothing but lots of too finely chopped fresh tuna.
 
Google Books
Between Honor and Duty
By Charlotte Maclay
New York, NY: Harlequin Books
2001
Pg. 149:
My mother’s a wonderful person but she can turn a hamburger patty into a hockey puck without even trying.
 
Google Books
The Barbecue America Cookbook:
America’s Best Recipes from Coast to Coast
By Rick Browne and Jack Bettridge
Guilford, CT: Lyons Press
2002
Pg. 6:
His first barbecue was a hamburger scorched black and about as tasty as a hockey puck, which is just what he used it for. He was in Canada, eh?
     
Google Books
The Great Big Burger Book:
100 New and Classic Recipes for Mouthwatering Burgers Every Day and Every Way
By Jane Murphy and Liz Yeh Singh
Boston, MA: harvard Common Press
2003
Pg. 2:
Pressing down on it while you cook it will only make the juices flow out — a sure-fire ticket to a dry hockey puck. 
   
Google Books
Mastering the Grill:
The Owner’s Manual for Outdoor Cooking
By Andrew Schloss and David Joachim
San Francisco, CA: Chronicle Books
2007
Pg. 10:
And they want the holy grail of grilling — to know how to make a simple, tender grilled hamburger rather than a charred hockey puck.