Bring a large pot of salted water to a boil and add spaghetti or bucatini. Cook according to package instructions until al dente, usually about 8-10 minutes. Reserve 1-1.5 cups of pasta water before draining.

In a large skillet, heat olive oil over medium-high heat until shimmering. Add shrimp, cooking for 1-2 minutes on each side until pink and opaque. Remove shrimp from skillet.

In the same skillet, add asparagus and sauté over medium heat for 3-5 minutes, stirring occasionally. Add minced garlic for the last 30 seconds and remove from heat.

In a medium bowl, whisk egg yolks, whole egg, and grated Pecorino Romano until well combined. Season with black pepper to create the sauce.

Add drained pasta to the skillet with sautéed vegetables. Pour in the egg and cheese mixture while tossing continually. Gradually add reserved pasta water to achieve creamy consistency.

Fold shrimp and asparagus back into the pasta, mixing gently. Adjust thickness with more reserved pasta water if necessary. Season with salt and pepper.

Plate your dish and garnish with extra cheese and parsley if desired. Serve immediately.