Place the walnuts and garlic in the bowl of a food processor fitted with a steel blade. Process until coarsely chopped.
Add the basil leaves, salt, and pepper and process until mixture resembles a paste.
With the processor running, slowly pour the olive oil through the feed tube and process until the pesto is thoroughly blended.
Add the parmesan and process a minute more.
Use pesto immediately or store in a tightly sealed jar. It will keep in the refrigerator for about a week.