Bring a large pot of salted water to a boil. Mix the Parmesan, egg yolks, 1/2 teaspoon salt and a generous amount of black pepper together in a medium bowl; set aside.
Snap off the woody ends of the asparagus stalks. Use a vegetable peeler to shave the asparagus into thin wide ribbons. (The last strip of asparagus will be a little thicker than the others, but it is fine to use.) Set aside.
Cook the fettuccine in the boiling water according to the package instructions for al dente. Reserve 1/2 cup of the pasta water, then drain.
Meanwhile, cook the bacon in a large skillet over medium-high heat, stirring occasionally, until crisp, 7 to 8 minutes. Drain off all but 2 tablespoons bacon fat from the skillet. Add the crushed red pepper flakes and garlic and cook, stirring, until fragrant, about 1 minute. Reduce the heat to medium low, add the drained pasta and asparagus and toss until well coated and mixed with the bacon.
Whisk 1/4 cup of the reserved pasta water into the egg mixture, then quickly pour it over the pasta and toss to gently cook the eggs and make a creamy sauce. Thin out the mixture with more pasta water as needed, 1 tablespoon at a time. Divide among 4 bowls and garnish with the parsley and more Parmesan if desired.
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