Cook the noodles by bringing a large pot of water to a boil and adding the udon noodles. Cook according to package directions, reserving ½ cup of noodle water before draining.

In a large skillet, melt 2 tablespoons of butter over medium heat. Add 3 minced garlic cloves and 1 chopped shallot, sautéing until fragrant and translucent.

Stir in 2 tablespoons of gochujang and cook for about 30 seconds. Then pour in ½ cup of heavy cream and the reserved noodle water, stirring until smooth.

Add 2 tablespoons of soy sauce and 1 teaspoon of gochugaru. Let it simmer for 3-5 minutes over low heat until it thickens.

Toss the cooked udon noodles into the sauce, gently folding until well coated and heated through.

Serve the noodles plated, sprinkled with grated parmesan and chopped green onions. Consider adding an egg yolk on top for extra richness.