Begin by bringing a large pot of salted water to a boil. In a medium bowl, whisk together the grated Parmesan, egg yolks, 1/2 teaspoon salt, and a generous amount of freshly ground black pepper. Set this mixture aside.

Trim the tough, woody ends from the asparagus stalks. Using a vegetable peeler, shave the asparagus into thin, wide ribbons. The final piece of asparagus may be slightly thicker, which is perfectly acceptable. Set the ribbons aside.

Cook the fettuccine in the boiling salted water according to the package directions, ensuring it is al dente. Reserve 1/2 cup of the pasta cooking water, then drain the pasta.

While the pasta cooks, place the bacon in a large skillet and cook over medium-high heat, stirring occasionally, until the bacon becomes crisp, approximately 7 to 8 minutes. Once done, drain off all but 2 tablespoons of the bacon fat. Add the crushed red pepper flakes and minced garlic, cooking for about 1 minute or until fragrant. Reduce the heat to medium-low, then add the drained fettuccine and asparagus, tossing until the pasta and asparagus are evenly coated with the bacon.

To make the sauce, whisk 1/4 cup of the reserved pasta water into the egg and Parmesan mixture. Quickly pour the egg mixture over the pasta, tossing gently to cook the eggs and form a creamy sauce. If the sauce is too thick, gradually thin it with additional pasta water, one tablespoon at a time. Serve the carbonara in bowls, garnished with freshly chopped parsley and more grated Parmesan, if desired.