In the bowl of a food processor, combine walnuts, garlic, lemon zest, lemon juice, cayenne, basil, Parmesan, salt and pepper and pulse until well blended.
With processor running, stream in olive oil until smooth, about 1 minute. If pesto is too thick, add more olive oil.
Transfer pesto to an airtight container and place a layer of plastic wrap on top of pesto to help prevent browning. Seal container and store in the refrigerator for up to a week.
