Toast walnuts by placing on a microwave safe plate. Microwave for 30 seconds. Stir and microwave again for another 30 seconds or until walnuts smell fragrant. Do not overcook. Allow walnuts to cool slightly..
Place basil, 1 tablespoon olive oil, walnuts, and parmesan cheese in a food processor.
Turn food processor on and drizzle with additional olive oil as the mixture processes until the desired consistency is reached.
Cook’s notes: For a more traditional pesto sauce, pine nuts can be substituted for walnuts.