Creamy Linguine with Brussels Sprouts

Bring an 8-quart stock pot of water to a boil and generously season with salt. Cook pasta according to al dente package instructions. Reserve 1 cup pasta water. In a large sauté pan over medium-high heat add drizzle of olive oil. Place half of the brussels sprouts cut side down and cook until dark golden brown, about 3 minutes. Toss and cook 1 minute more, then season with salt and pepper. Transfer to a plate and repeat process for remaining brussels sprouts. Set aside. Heat sauté pan over medium-low heat with drizzle of olive oil; sauté garlic for 2 minutes. Add white wine, chili flakes, brussels sprouts 1/2 teaspoon salt, and 1/4 teaspoon black pepper. Transfer pasta to pan and toss together until well coated. Turn off heat and mix in cheese, parsley, and egg yolk, mixing quickly using tongs. If you want a thinner sauce add reserved pasta water slowly until desired consistency. Drizzle with olive oil and garnish with parsley and cheese. Serve immediately.