1. Bring a large pot of water to boil.
2. Snap tough ends off asparagus. Cut stems into 1-in pieces and reserve tips separately.
3. Add 2 tablespoons salt and asparagus stems to boil water. Cook
stems until very tender, 6 to 8 minutes. Remove stems with a
slotted spoon and refresh under cold running water. Reserve.
4. Add asparagus tips to boiling water and cook until tender, 3 minutes. Remove with a slotted spoon and refresh under running water. Reserve tips (still keeping them separate stems) and asparagus-cooking water.
5. In food processor, combine reserved asparagus stems, oil, lemon
zest and 1/2 cup asparagus-cooking water. Process until smooth.
Season with salt and pepper. Trans to a 4 quart pot.
6. Return the remaining asparagus-cooking water to a boil, add pasta
and cook until not quite al dente, 8 to 10 minutes.
7. Drain, reserving 1 cup of pasta water. Add pasta, asparagus tips and 1/2
cup reserved pasta water to asparagus puree.
8. Cook, stirring, over high heat until the pasta is al dente and the sauce coasts it, 3 to 5 minutes. Add more pasta-cooking water, 1/4 cup at a time, if the sauce becomes too dry.
9. Stir in 1/4 c. Parmesan. Serve, passing remaining parmesan.