Wash and dry the fresh produce. Thinly slice the mushrooms. Thinly slice the scallions, separating the white bottoms and hollow green tops. In a bowl, whisk together the miso paste, béchamel, 1/4 cup of water (or 1/2 cup for 4 servings), and as much of the gochujang as you'd like, depending on how spicy you'd like the dish to be; season with salt and pepper. Stir to combine.

In a large nonstick pan, heat a drizzle of olive oil on medium-high until hot. Add the pork; season with salt and pepper. Cook, stirring frequently and breaking the meat apart with a spoon, 3 to 4 minutes, or until lightly browned. Carefully drain off and discard any excess oil. Add the sliced mushrooms and sliced white bottoms of the scallions; season with salt and pepper. Cook, stirring occasionally, 2 to 3 minutes, or until lightly browned and slightly softened.

Using your hands, carefully separate the rice cakes. To the pan, carefully add the rice cakes and sauce; season with salt and pepper. Cook, stirring frequently, 1 to 2 minutes, or until combined and the rice cakes are tender. Add the cheddar and monterey jack. Cook, stirring frequently, 1 to 2 minutes, or until the cheese is melted and the pork is cooked through. Serve the finished rice cakes topped with the kimchi and sliced green tops of the scallions. Enjoy!