Place fresh basil leaves, walnuts, garlic, salt, black pepper, Parmesan cheese, lemon juice, and 2 tablespoons of olive oil into a small food processor.
Blend the ingredients until the mixture is finely chopped.
With the food processor running, slowly drizzle in the remaining olive oil until the pesto reaches a slightly coarse, saucy consistency. Add more olive oil if needed to achieve your preferred texture.
Pause occasionally to scrape down the sides of the bowl, ensuring everything blends evenly. Taste and adjust the seasoning, adding more salt if needed.
Your pesto is now ready to use! If not using immediately, transfer it to an airtight container and refrigerate for up to one week.
Notes
To help prevent oxidation, cover the surface with a thin layer of olive oil or press a piece of plastic wrap directly onto the pesto.