We were told by our guide, Miss Sakinah Omar, that another halal food that we could try in Jeju was bab (rice) burger. It looked like a burger, except the buns were replaced by rice that was formed in the shape of buns. While, the patty inside would be variety of filling. As for us, we chose, squid in meshed chilies. So for Muslim travelers, you definitely have to choose the right filling to go with your rice, which should be something definitely from the seafood family.
The squid actually tasted so much like our local "sambal sotong" so I had somehow enjoyed my dinner. I guess if you are having a Korean as a guest at home, he/she will have no problem eating any dish with meshed chilies.
I also bought the seafood triangle rice cake, known as Onigiri in Japan, but I did not know what it is called in Korea.