Put a large pan of water on to boil. Peel asparagus, and break off tough bottoms. Cut off tips at about 2 inches, but keep stalks in one piece. Salt boiling water, add asparagus stalks, thickest ones first, and boil until half done. Add tips and continue boiling until tender but still crisp, stiff and bright green.
Test as you go along. Remove and cool slightly. Cook the pasta in the asparagus water. Melt butter in a frying pan and saute prosciutto until the butter begins to brown, but don't crisp the prosciutto. Add cream and bring back to the boil, scraping the prosciutto bits off the bottom. Grind in some fresh pepper. Slice asparagus stalks into 2 inch lengths.
Add to the sauce with the tops and stir to coat; the cream should have reduced and thickened. Drain pasta when it is al dente and turn into a warm serving bowl. Mix in the sauce and the Parmesan, toss gently, and taste for salt and pepper before serving.