Preheat the broiler to 500 degrees F
Heat the skillet over medium-high. Add the oil. Drain and fry up the rice cakes, until they've taken on a golden color, and set aside.
Mix the chicken, onions, peppers, gochujang, gochugaru, garlic, ginger, soy sauce/tamari, rice syrup/honey, and black pepper together. While you can marinate, it can be cooked directly.
Fry up the chicken and veggies in the skillet over medium-high, until the chicken is cooked through, and the vegetables are slightly softened.
Add 1/2 c water and the rice cakes, and simmer for 5 minutes, until the sauce starts to thicken. Add water as needed to maintain a slightly fluid consistency.
Generously top the skillet with mozzarella or cheese substitute. Pop in the broiler for 5 minutes, or until the cheese is gooey and melted.
Serve with green onions!