Cut asparagus into 1-inch pieces; reserve tips separately. Cook asparagus stems in 5 to 6 quarts boiling water with 2 tablespoons salt until very tender, 6 to 8 minutes. Transfer with a slotted spoon to a colander, reserving cooking water in pot, and rinse under cold water. Drain asparagus well and transfer to a food processor or blender.

Cook asparagus tips in same boiling water until just tender, 3 to 5 minutes. Transfer with slotted spoon to colander, reserving boiling water in pot, and rinse under cold water. Drain tips well.

Puree asparagus stems with zest, oil, and 1/2 cup asparagus cooking water. Transfer sauce to a 4-quart saucepan.

Cook pasta in boiling asparagus cooking water for about three-fourths of the recommended cooking time (very al dente). Reserve 2 cups cooking water and drain pasta.

Add pasta, asparagus tips, and 1/2 cup reserved water to asparagus sauce and cook over high heat, stirring, 3 to 5 minutes, or until pasta is almost al dente and sauce coats pasta. Add more cooking water, 1/4 cup at a time, until sauce coats pasta but is a little loose (the cheese will thicken it slightly).

Stir in Parmigiano-Reggiano and salt and pepper, to taste and cook, stirring, until cheese is melted. Serve immediately