Add walnuts, parmesan, lemon zest, and garlic into a food processor. Pulse until finely chopped.
Add basil leaves and pulse until finely chopped. Scrape down the sides of the bowl as needed.
With the food processor running at low speed, add the olive oil in a slow and steady stream until the oil is incorporated.
Season to taste with salt and pepper. If you'd like your pesto sauce thinner, just add more olive oil.
Serve and enjoy!