Prepare pasta according to package directions, cutting back 2 minutes on cooking time. Drain, reserving 1/2 cup of the pasta water.
While pasta is cooking, bring 1/4 cup salted water to a boil in a large skillet over medium-high heat. Add asparagus, cover and cook for 3-5 minutes, or until asparagus is just crisp-tender. Drain into a colander, and return pan to heat.
Swirl in oil and, when hot, add garlic and prosciutto. Sauté for 1 minute, and add asparagus back to pan. Continue cooking another 2-3 minutes, stirring occasionally, until asparagus just begins to char in places, and garlic and prosciutto have crisped.
Meanwhile, in a small bowl, whisk together 2 tablespoons reserved pasta water, egg yolk, Parmesan cheese and chicken stock.
Return drained pasta to pot over medium-low heat. Add egg mixture and toss. Add asparagus mixture, salt to taste, and toss again. Cook 2 minutes, or until sauce thickens and starts to stick to pasta, adding additional pasta water by tablespoon intervals if sauce seems dry. Toss with parsley just before serving.