Bring a large pot of salted water to a boil. Add the pasta and cook according to the package directions.
While the pasta is cooking, make the pistachio pesto. Combine the pistachios, basil, olive oil, Parmesan, garlic, lemon zest and juice and some salt and pepper in a food processor and process until well combined.
Reserve 1 cup of the pasta water and drain the pasta. Toss the pasta with the pistachio sauce, thinning with the pasta water for the desired consistency if necessary. Serve with more Parmesan and basil leaves.