Toast walnuts in the oven at 375 ° or until lightly toasted and fragrant and let cool. In the bowl of a food processor with a metal blade, process walnuts, garlic, and salt and pepper until very finely chopped. Add in basil leaves and pour olive oil through the feed tube until desired consistency. Stop to scrape down the sides if necessary. Add the Parmesan cheese and process for 30 seconds or so. Store in refrigerator or freezer with a thin layer of olive oil to prevent browning.