Combine the hot pepper flakes, hot pepper paste, soy sauce, 2 tablespoons of vegetable oil, black pepper, sugar, garlic, and ginger in a large bowl. Mix well. Add the chicken. Mix with a spoon until it’s evenly coated.

Heat a medium-sized oven-safe skillet over medium-high heat. Add the remaining 1 tablespoon of oil and the rice cakes. Cook for 3 to 4 minutes, turning with a spatula, until the edges of the rice cakes turn light golden. Transfer the rice cakes to a small bowl.

Add the chicken, salt, and ¼ cup of water into the same skillet. Cover and cook, stirring occasionally, for 7 to 8 minutes.

Add the rice cakes and stir to mix well. Reduce the heat to low. Cover and cook for 5 minutes, until the chicken is fully cooked.

While the chicken is cooking, preheat the broiler in the oven, with the rack positioned on the middle level.

Spread the mozzarella cheese over the chicken. Transfer the skillet into the oven under the broiler. Broil until the cheese is melted completely, bubbling and lightly charred. Keep an eye on it closely, checking every minute or two.

Remove the skillet from the oven and let it sit for 5 minutes to let the cheese set. Serve hot as a main dish.

The dish can be made in advance and warmed up in a 350 °F (176 °C) oven. You can heat up the leftovers in the microwave or in the oven.