Soak the Rice Cakes: Place the rice cakes in a bowl of warm water and let them soak for about 10-15 minutes to soften. Drain and set aside.
Prepare the Sauce: In a large skillet or saucepan, heat the vegetable oil over medium heat. Add the minced garlic and sauté until fragrant, about 1 minute.
Add Flavorings: Stir in the gochujang (Korean red chili paste), soy sauce, sugar, and a splash of water. Mix well to combine all the ingredients into a cohesive sauce.
Simmer: Pour in the remaining water and bring the mixture to a gentle simmer. Allow it to cook for 3-5 minutes, letting the flavors meld together.
Add Rice Cakes: Add the soaked rice cakes to the skillet, ensuring they are submerged in the sauce. Let them cook for 5-7 minutes, stirring occasionally, until they become tender and have absorbed the flavors.
Incorporate Cheese: Reduce the heat to low and evenly sprinkle the shredded mozzarella and cheddar cheeses over the rice cakes. Cover the skillet and let it sit for 2-3 minutes, or until the cheese has melted and become gooey.
Garnish and Serve: Drizzle the sesame oil over the top, then sprinkle with toasted sesame seeds and chopped green onions. Serve hot and enjoy your homemade cheese rice cakes!