Bring a large pot of water to a boil, salt it, add the pasta and cook until al dente. Add the asparagus in the last 2 minutes of cooking. Drain, reserving 1 cup of the pasta cooking water.
While the pasta is working, in a large skillet, heat the EVOO, 4 turns of the pan, over medium heat. Add the prosciutto and cook for 2 minutes. Lower the heat to medium-low and stir in the garlic for 2 minutes. Add the wine and cook until reduced slightly, 1 minute. Lower the heat to the lowest setting.
In a medium bowl, combine the reserved pasta cooking water and the beaten egg yolks to temper the eggs. Add the drained pasta to the prosciutto mixture in the skillet. Season with the cheese, thyme, lemon peel and pepper. Pour in the egg mixture and toss vigorously to thicken the sauce, 1 to 2 minutes. You can add a small squeeze of lemon juice to the dish to emphasize the citrus flavor if you like.