1 cup finely chopped kimchi, plus ⅓ cup kimchi juice
2 tablespoons gochujang (Korean hot pepper paste)
½ cup low-sodium chicken broth
1 pound fresh or frozen udon noodles
4 large egg yolks, room temperature
3 scallions, white and pale-green parts only, thinly sliced on a diagonal
1 tablespoon toasted sesame seeds
Heat 1 Tbsp. butter in a large skillet over medium-high. Add chopped kimchi and gochujang and cook, stirring occasionally, until kimchi is softened and lightly caramelized, about 4 minutes. 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.
Using tongs, transfer noodles to skillet; cook, tossing often, until sauce coats noodles, about 2 minutes. Season with salt if needed. Divide among bowls and top with egg yolks, scallions, and sesame seeds.