Place basil leaves in small batches in food processor and whip until well chopped (do about 2/3 cup at a time). Add about 1/3 the nuts and garlic, blend again.
Add about 1/3 of the Parmesan cheese; blend while slowly adding about 1/3 of the olive oil, stopping to scrape down sides of container.
Process basil pesto until it forms a thick smooth paste. Repeat until all ingredients are used, mix all batches together well. Serve over pasta.
Basil pesto keeps in refrigerator one week, or freezer for a few months.