A popular Christmas riddle about elves is:
 
Q: What kind of bread do elves make sandwiches with?
A: Shortbread.
 
The riddle has been cited in print since at least 1998.
 
“Shortbread—They’re not making it any longer” is another shortbread joke.
   
 
Wikipedia: Shortbread
Shortbread is a type of biscuit (American English: cookie) traditionally made from one part white sugar, two parts butter, and three parts flour (by weight). The use of plain white (wheat) flour is common today, and other ingredients like ground rice or cornflour are sometimes added to alter the texture. Also, modern recipes often deviate from the pure three ingredients by splitting the sugar portion into equal parts granulated sugar and icing sugar (powdered sugar in American English) and many further add a portion of salt.
 
Shortbread is different from shortcake, though they are similar. The difference is that shortcake can be made using vegetable fat instead of butter and usually has a chemical leavening agent such as baking powder, which gives it a different texture. Shortbread biscuits are often associated with normal egg-based biscuits, but they hold their shape under pressure, making them ideal for packed meals.
 
Shortbread originated in Scotland, with the first printed recipe, in 1736, from a Scotswoman named Mrs McLintock. Shortbread is widely associated with Christmas and Hogmanay festivities in Scotland, and the Scottish brand Walkers.
     
Google Groups: alt.teens.penpals
A Question I have about sex
merry mcgrath
8/24/98
Laugh Lines from the sexually un-damaged:  1.  What do elves use to make sandwiches?  Shortbread.
   
5 December 1999, Los Angeles (CA) Times, “The Kids’ Reading Room; Reading by 9; Jokes & Riddles,” pg. E8:
What do elves use to make sandwiches? Shortbread. (Taryn, 8, North Hollywood)
 
Google Groups: alt.teens.penpals
Hey, Shorty.
merry mcgrath
12/8/99
What do elves use to make sandwiches?  Shortbread.
 
Google Groups: alt.humor.puns
Puns of the Weak 11-14-03 Part 2 The Puns
Stan Kegel
11/15/03
(...)
What do elves make sandwiches with?
Shortbread! (Daily Groaner)
 
Google Groups: rec.food.sourdough
OFF TOPIC: What kind of bread to elves make their sandwiches with?
Dick Adams
6/10/08
Shortbread!
 
Twitter
David Crank
‏@davidcrank
What kind of bread do elves make sandwiches with?
Why, shortbread of course!
 
What kind of money do elves use?
Jingle bills!
5:01 PM - 11 Dec 2009
   
Google Books
Christmas Jokes
Illustrated by Jane Eccles
London: Pan Macmillan
2013
Pg. ?:
What kind of bread do elves make sandwiches with?
Shortbread.
 
Google Books
Christmas Cracker Jokes
By Amanda Li
London: Pan Macmillan
2014
Pg. ?:
What kind of bread do elves make sandwiches with?
Shortbread.
   
Google Books
Christmas Elf Jokes For Kids
By Peter Crumpton
PeteyRF Creative
2015
Pg. ?:
What kind of bread do elves make sandwiches with?
Why, shortbread of course!