Wash and dry the fresh basil leaves, ensuring they are clean and free of moisture.
In a food processor, combine the basil, Parmesan cheese, walnuts, and peeled garlic cloves.
Pulse the ingredients a few times until coarsely chopped.
With the food processor running, gradually add the olive oil in a steady stream. Continue processing until the mixture becomes smooth and well combined.
Season the pesto with salt and black pepper, adjusting to taste. If you prefer a saltier flavor, you can fold in a bit more of the Parmesan cheese.
If the pesto is too thick, you can add more olive oil until you reach your desired consistency.
Transfer the fresh basil pesto to a jar or airtight container. It can be stored in the refrigerator for up to a week. Alternatively, use it immediately as a sauce for pasta, a spread for sandwiches, or a topping for grilled meats.