Pesto:
Cook 1 cup peas until tender. In a food processor, combine cooked peas, parsley, walnuts, Parmesan, garlic and 1 tablespoon water. Pulse until a paste forms. With machine running, slowly add oil, processing until blended; season with salt and pepper.
Pasta:
In a large pot of boiling salted water, cook pasta according to package instructions, adding 1 cup peas 30 seconds before the pasta has finished cooking. Reserve 1 cup pasta water; drain pasta and peas. Return pasta and peas to pot; toss with ¾ cup pesto (reserve remainder for another use). Adding enough pasta water to create a sauce that coats the pasta. Season generously with salt and pepper. Serve pasta with more Parmesan.