Prepare the Tteok (Rice Cakes)

1. Soak the Rice Cakes: If using frozen rice cakes, soak them in warm water for about 10-15 minutes to soften them up. Fresh rice cakes don’t require soaking.
2. Heat the Pan: In a large skillet or saucepan, heat the sesame oil over medium heat. Add the minced garlic and sauté for 1-2 minutes until fragrant.

Make the Sauce

1. Add the Liquid: Pour in the water, followed by the gochujang, gochugaru, soy sauce, and sugar. Stir well to combine, making sure the gochujang dissolves completely.
2. Simmer the Sauce: Bring the sauce to a simmer and let it cook for 2-3 minutes, stirring occasionally. This will allow the flavors to meld together.

Cook the Rice Cakes

1. Add the Rice Cakes: Drain the soaked rice cakes (if using frozen) and add them to the simmering sauce. Stir to coat the rice cakes evenly with the sauce.
2. Cook the Tteok: Let the rice cakes cook in the sauce for about 5-7 minutes, or until they become soft and absorb the flavors of the sauce. If the sauce reduces too much, add a bit more water to achieve the desired consistency.

Add the Fish Cake (Optional)

1. Incorporate the Fish Cake: If you’re using fish cake, slice it into thin pieces and add it to the pan with the rice cakes. Stir well to incorporate.

Add the Cheese Topping

1. Top with Cheese: Sprinkle the shredded mozzarella cheese generously over the rice cakes. Add the Parmesan cheese for an extra savory touch if desired.
2. Melt the Cheese: Reduce the heat to low, cover the pan with a lid, and let the cheese melt for 2-3 minutes. You can also put the pan under the broiler for 1-2 minutes if you like a crispy, golden cheese topping.
3. Add Butter: For an extra creamy touch, stir in a little bit of butter just before serving.