Place the rice cakes in a large bowl and submerge them in warm water. Let them soak for at least 5 minutes to soften and adjust to room temperature. Drain thoroughly and set aside.

Heat a non-stick pan over medium heat, without adding oil. Add the sliced bacon and cook until it reaches a partially crispy texture. Once halfway cooked, add the chopped green onions and minced garlic. Stir-fry for about 20 seconds, allowing the green onions to release their fragrant aroma.

Pour in the milk or heavy cream, then incorporate the gochujang, gochugaru, sesame oil, and soy sauce. Stir continuously until the sauce transforms into a rich rose-colored mixture, ensuring that the ingredients meld together smoothly.

Add the fish cakes and drained rice cakes into the pan. Lower the heat to a gentle simmer and allow the sauce to thicken, stirring occasionally to prevent sticking. Keep the pan uncovered to help the sauce develop a creamy consistency.

Once the sauce has reduced and turned velvety, and the rice cakes have softened to a chewy texture, sprinkle the mozzarella and Swiss cheese over the top. Let the residual heat melt the cheese into the sauce, creating a luscious, gooey finish. Garnish with additional chopped green onions, if desired. Serve immediately and enjoy!