Cut the asparagus into 1/2-inch slices on the diagonal, so each piece of asparagus is cut into 3 pieces.
In a large pot bring 5 quarts salted water to a boil. Add the pasta and cook until al dente. For a pasta cooking guideline, I subtract 1 minute from the suggested cooking time on the box.
While the pasta is cooking prepare the sauce: In a deep 12-inch skillet, heat butter and cream over moderately low heat until butter is melted. Whisk in zest, lemon juice, and salt. Remove skillet from heat and keep sauce warm, covered.
When the pasta is finished, ladle 1/4-cup pasta water into sauce. Drain the pasta in a colander.
Immediately add pasta and asparagus to sauce and cook over moderate heat, tossing, 3-5 minutes, until pasta is heated through and asparagus is fork tender. Add basil, salt and pepper to taste, and toss well.Add freshly grated Parmesan to the pasta and serve.