1.Rinse the rice cakes and drain. Set aside. In a small pot cook eggs until they are hard boiled then cut each one into quarters, set aside.
2.Place the bacon in a cold large skillet and cook over medium heat until crispy and the fat is rendered, about 5 minutes. Remove the bacon from the pan with a slotted spoon and set aside.
3.In the same pan with the bacon fat, cook the garlic over medium heat for just a minute to toast it. Add the rinsed rice cakes, water, dashi, gochugaru, gochujang, sugar, soy sauce, fish sauce, and mirin. Stir until all combined.
4.Bring to a boil, lower the heat to simmer and add the fish cakes and cabbage. Cook until the rice cakes are tender and the sauce thickens, 3 to 5 minutes.
5.Add green onions and then stir well. Add the American cheese and mozzarella and stir to melt them into the sauce. Remove from the heat and top with the crispy bacon and the quartered hard-boiled eggs. Serve immediately.