Korean foods are often naturally gluten-free as long as you use gluten free soy sauce. Which means there's no loss of deliciousness when it comes to gluten free Korean foods.
For gluten-free soy sauce, make sure you buy a gluten-free soy sauce (Kikkoman makes some) or Tamari sauce is another option.
Japchae, Yaksik (Sweet Rice Dessert), Korean Fried Chicken and any Namuls like Mungbean Sprouts (Sukju Namul) are all gluten-free and a must-try!