Cook 1 cup peas according to package instructions. 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.
In a large pot of boiling salted water, cook pasta according to package instructions, adding 1 cup peas 30 seconds before end of cooking. Reserve 1 cup pasta water; drain pasta and peas. Return pasta and peas to pot; toss with 3/4 cup pesto (reserve remainder for another use), adding enough pasta water to create a sauce that coats pasta. Serve pasta with more Parmesan.
For pasta anytime, freeze extra pesto in ice-cube trays, up to 3 months; thaw before using.