Add basil, lemon zest, lemon juice, walnuts, parmesan, salt, and pepper to a food processor. Pulse a few times until the nuts and basil are all chopped to about the same size.

Drizzle in the olive oil and puree until smooth. Add less olive oil if you like a thicker pesto or add more if you like a thinner pesto.

Store in an airtight container in the refrigerator for two weeks or freeze for up to two months.