Here's my list of must eats in Seoul...I really only spent a few short hours roaming the streets and alleys of Insadong so I'm sure this list is lacking...but don't worry, eventually I will head back for more research :)
 
Sweet:

Jipangei ice cream: Ice cream in a funny shaped cone tube made of corn cake, take a look and try to not let your imagination get the best of you. Order the Vanilla...SO good. Reminds me of a chick-fil-a ice dream. Dreamy indeed!