Cut rice cakes, fish cakes, and onions into bite-sized pieces.
Heat cooking oil in a pan and sauté the onions.
Add the rice cakes and fish cakes, stir-fry together.
Add gochujang, chili powder, sugar, soy sauce, and water, then bring to a boil.
When the rice cakes become soft, add the rice and mix well.
Add the beaten eggs and scramble lightly.
Top with mozzarella cheese and let it melt.
Transfer the finished tteokbokki cheese egg rice to a bowl.