Bring a large pot of water to a boil. Add udon noodles and cook according to package instructions for 8-10 minutes. Reserve ½ cup of starchy noodle water, drain and rinse noodles.

In a large skillet, melt butter over medium heat. Add minced garlic and chopped shallot. Sauté for about 2-3 minutes until fragrant and translucent.

Stir in gochujang and cook for an additional 30 seconds to 1 minute.

Pour in heavy cream and reserved noodle water. Add soy sauce and gochugaru. Simmer for 2-3 minutes until thickened.

Add cooked udon noodles to the sauce and toss for 1-2 minutes to coat.

Serve in bowls, garnished with parmesan cheese, green onions, and optional egg yolk.