Heat a large pot over medium-high heat. Add a tablespoon of canola oil. Add the kimchi and king oyster mushrooms. Cook until the mushrooms have softened, about 5 minutes.
Add the gochujang, gochugaru, sugar, sake, and kimchi juice. Mix until well combined. Add the broth and aka miso, stir until everything is mixed together.
Place the cabbage, tofu, pork meatballs, enoki mushrooms, shimeji mushrooms, and scallions into the pot.
Allow the broth to come to a slight boil. Reduce the heat and simmer until the meatballs are cooked through, about 10 minutes. Serve with udon.