Bring a large pot of water to a rolling boil over high heat. Add the udon noodles and cook according to the package instructions, typically 4-10 minutes. Reserve ½ cup of noodle water and drain the rest.

In a large skillet, melt 2 tablespoons of butter over medium heat. Add minced garlic and chopped shallots, sautéing for 2-3 minutes until translucent.

Add 2 tablespoons of gochujang to the skillet and cook for about 30 seconds until it starts to bubble.

Reduce heat to low and pour in 200 ml of heavy cream along with the reserved noodle water. Stir to combine and let simmer for 3-4 minutes.

Carefully add the cooked udon noodles to the skillet and gently toss in the creamy gochujang sauce for 2-3 minutes.

Divide the creamy udon noodles into serving bowls and top with grated Parmesan cheese and green onions.