In a 6- to 7-quart kettle bring about 5 quarts salted water to a boil for pasta.
Have ready a bowl of ice water. Trim woody ends from asparagus. Cut asparagus stalks crosswise into 2-inch pieces, reserving tips. In a steamer set over boiling water steam stalks, covered, 4 minutes. Add reserved asparagus tips and steam, covered, until just tender, about 1 minute. Immediately transfer asparagus to ice water to stop cooking. Drain asparagus well in a colander and pat dry.
In a food processor pulse pine nuts and garlic with salt until finely chopped. Add asparagus and oil and pulse until asparagus is coarsely chopped. Transfer pesto to a large bowl and stir in Parmigiano-Reggiano. Cook pasta in boiling water until al dente. Reserve 1/3 cup pasta cooking water and drain pasta in a colander. Add pasta and reserved cooking water to pesto, tossing to coat, and season with salt and pepper.
