Bring a pot of water to a boil and cook frozen udon noodles according to package instructions. Once cooked, reserve ½ cup of noodle water and set it aside. Drain the noodles, rinse under cold water, and set them aside.

In a pan, melt butter over medium heat. Add the minced garlic and chopped shallots and sauté until fragrant. Add gochujang and cook for about 30 seconds.

Slowly pour in the heavy cream and reserved noodle water, then add soy sauce and gochugaru. Mix and bring the sauce to a simmer. Let it simmer for a few minutes until thickened.

Add the cooked udon to the pan, toss to coat them evenly in creamy gochujang sauce.

Transfer the noodles to a bowl. Top with grated parmesan cheese, chopped green onion, and an egg yolk. Serve hot and enjoy!