1. In a large pot of boiling salted water, cook pasta according to package instructions, adding the asparagus in the last two minutes of cooking. Reserve 1 cup cooking liquid (you won’t use all of it!); drain pasta and asparagus and return to pot along with butter and Parmesan. Toss until butter is melted, adding enough pasta water to create a thin sauce that coats pasta.
2. While pasta is cooking, fry eggs over easy.
3. To serve, divide pasta among four bowls, top each serving with an egg and season with salt and pepper. Sprinkle with Parmesan if desired.