Cook the frozen udon noodles according to package instructions (3-5 minutes in boiling water). Reserve ½ cup noodle water, drain, and rinse noodles under cold water.

Melt 2 tablespoons of butter in a skillet over medium heat. Add 2 cloves of minced garlic and 1 chopped shallot, stirring until fragrant and translucent (2-3 minutes).

Stir in 3 tablespoons of gochujang, cooking for 30 seconds. Gradually add ½ cup heavy cream and reserved noodle water, whisking to create a smooth sauce. Stir in 1 tablespoon soy sauce and 1 teaspoon gochugaru, simmering until thickened (2-3 minutes).

Add cooked udon noodles to the skillet, tossing gently to coat in sauce.

Serve in bowls, topping with grated Parmesan cheese, chopped green onions, and an egg yolk if desired.