When it comes to ice cream in Korea, I think the best place to start is patbingsu. Shaved ice with jellied/fresh fruit and sweet red beans. Above is prepackaged patbingsu you can pick up in the ice cream section.
And this is patbingsu that was put together at a shop, but packaged for takeout. Definitely much better than the prepackaged one above.
Keeping it traditional Korean style, there are ice cream rice cakes! The green part is rice cake and the inside is ice cream. Totally delicious, but I don't see it in shops as often.