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Place basil leaves in small batches in food processor and whip until well chopped (do about 3/4 cup at a time). Add about 1/3 the nuts and garlic, blend again.
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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.
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Process basil pesto 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 freeze for a few months.
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Remove 1/2 cup of the cooking liquid before draining the pasta. Toss pasta immediately with the pesto sauce and the reserved cooking liquid. Serve at once with additional cheese, if desired.