Cook pasta according to package directions in heavily salted water. Scoop out a cup of pasta water before you drain it.
While the pasta is cooking, make the pesto: process the parsley and walnuts until well chopped. Add the cheese and pulse a few times. Now pour the oil through the feeder tube while the processor is running until the pesto is smooth.
Toss the hot pasta with the pesto, adding the pesto in increments until you have the amount you like on your pasta (you may have some leftover, which is a wonderful thing!). Add a little pasta water until the pasta has a light sauce.
Serve garnished with a little chopped parsley and fresh ground pepper.