Cook the udon noodles according to the package instructions, typically boiling for 5–7 minutes until tender but still chewy. Reserve about ½ cup of the starchy noodle water, then drain and rinse under cold water.

In a large skillet, melt 2 tablespoons of butter over medium heat. Add 2 minced garlic cloves and 1 chopped shallot, sautéing for about 3–4 minutes until fragrant and slightly golden.

Stir in 3 tablespoons of gochujang, cooking for about 30 seconds until fragrant, stirring continuously to prevent burning.

Gradually pour in 1 cup of heavy cream and the reserved noodle water, mixing well. Add 2 tablespoons of soy sauce and 1 teaspoon of gochugaru, then simmer for about 3–5 minutes until creamy.

Add the cooked udon noodles to the pan, tossing gently in the sauce for about 1–2 minutes to ensure even coating.

Transfer to serving bowls and top with grated Parmesan cheese and chopped green onions. Serve hot.