The original recipe is from Bon Appetit but I added a few more ingredients: fish sauce, soy sauce and kewpie mayo and reduced the amount of gochujang added.
Heat 2 tablespoons of butter in a large skillet over medium-high heat. Add chopped kimchi and gochujang and cook, stirring occasionally, until kimchi is softened and lightly caramelized, about 4 minutes. Add the soy sauce and fish sauce and stir until incorporated. Add broth and kimchi juice and bring to a simmer. Cook until liquid is slightly reduced, about 3 minutes.
Meanwhile, boil noodles according to package directions. Cooking time for udon noodles is usually 1 to 2 minutes only.
Using tongs, transfer udon noodles to skillet and add remaining 2 to 3 tablespoons butter and the kewpie mayo and toss together until the sauce coats the noodles, about 2 minutes. Divide among bowls and garnish with scallions. Enjoy!