Pluck basil leaves from stems (about 2 cups). Wash the leaves in a large bowl of cold water and dry in a salad spinner or pat dry with paper towels.
Put the basil, garlic, and pine nuts in a food processor and pulse until coarsely chopped. With the processor running, gradually add the olive oil and process until the pesto is smooth. Transfer the pesto to a large bowl and stir in the cheese. Season with salt and pepper.