In a food processor or a blender, process walnuts and garlic until coarsely chopped. Add basil leaves and pulse a few times to break the basil.

In a steady stream add olive oil, pulsing until the pesto is thoroughly blended. Add parmesan cheese, salt, and pepper and pulse again until thoroughly blended.

Use pesto immediately or store it in a tightly sealed container. Cover the top with a thin layer of olive oil to prevent it from oxidizing.