I think that food is an important part for travellers.
Here are my recommendations of Jeju food you may want to try
 
Black Pork BBQ
 
 
 
Abalone Porridge
 
 
 Grilled tile fish
 
 
Abalone Stew
 
 
Chicken soup with Ginsang
 
 
Sashimi - Raw fish
 
 
Pork Noodle - Jeju local noodle