Bring a large pot of water to a rolling boil. Add the frozen udon noodles and cook according to package instructions for 3-5 minutes. Reserve ½ cup of noodle water, drain, and rinse noodles.

Melt 2 tablespoons butter in a non-stick pan over medium heat. Add minced garlic and chopped shallot, sauté for 2-3 minutes until fragrant.

Stir in 2 tablespoons gochujang, mixing well for about 30 seconds until aromatic.

Pour in 1 cup heavy cream and the reserved noodle water, stirring continuously. Add 1 tablespoon soy sauce and 1 teaspoon gochugaru, simmer for 3-4 minutes to thicken.

Gently fold in the noodles, tossing to coat. Cook for an additional 1-2 minutes over low heat.

Serve in bowls, garnished with grated Parmesan, chopped green onions, and optional egg yolk.