“How did the eggs leave the highway?”/“They went through the ‘eggs-it’.”

An egg riddle (popular at Easter) is:
 
Q: How did the eggs leave the highway?
A: They went through the “eggs-it.”
 
The joke has been cited in print since at least 2003.
 
   
Google Books
Funny Riddles
By Jacqueline Horsfall
Illustrated by Steve Harpster
New York, NY: Sterling Publishing Company
2003
Pg. 31:
Where do chickens get off the highway?
At the eggs-it.
   
SearchWarp
List of the Best Easter Bunny Funny Jokes, Cute One Liners, and Cheesy Riddles.
By Sacreeta
FEBRUARY 16, 2008
(...)
How did the eggs leave the highway?
They went through the “Eggs-it”.
   
Twitter
G. Wayne Clayton‏
@SocialMtgExpert
Easter HAHA: Q: How does the Easter Bunny get off the highway on his way to deliver eggs?  A: He goes through the eggs-it.
5:02 PM - 12 Apr 2009
 
Twitter
Jet AKA Bok Bok‏
@JetakaBokBok
Joke of the day! Q. How did the eggs leave the highway? A. They went through the “Eggs-it”
4:24 PM - 7 Oct 2009
   
Its All Humor
Wednesday, March 31, 2010
Easter egg jokes
(...)
Q. How did the eggs leave the highway?
A. They went through the “Eggs-it”.
   
Google Groups: comp.sys.hp.mpe
OT : Easter bunnies..
Rao, Raghu
4/1/10
(...)
How did the eggs leave the highway?
They went through the “Eggs-it”.
 
Google Books
The Mammoth Book of Really Silly Jokes
Edited by Geoff Tibballs
London, UK: Constable & Robinson, Ltd
2011
Pg. 79:
How did the eggs leave the highway?
They went through the eggs-it.
 
26 April 2011, The Northern Star (Lismore, New South Wales), “Jokes by Kristi-Lee Gollan, age 11. Kristi-Lee has won a $10 Blast Off Voucher,” pg. 24:
Q. How did the eggs leave the highway?
A. They went through the eggs-it.
 
Twitter
HBplayz11‏
@pyrateshiphb
How do eggs leave the highway? By going through the eggs-it. #Egghunt2017 plz read on liuve stream im on it 😁😁😁😁😁😁
7:46 PM - 7 Apr 2017