In a food processor fitted with blade, process basil leaves, and pine nuts with a few pulses.
With food processor running, add chopped garlic, and slowly drizzle olive oil, stopping to scrape down the sides of the bowl.
Add cheese, and pulse for a few seconds, taste and adjust seasoning, adding black pepper and salt if necessary.
Fill a large pot with salted water, and bring to a boil. Add fusilli.
Cook pasta a minute or two LESS than the package directions. You do not want to over-cook the pasta as you will finish cooking it on the stove with the sauce. Just before draining pasta, reserve about 1 cup of pasta water.
Toss the pasta with some of the sauce and a small ladle of the pasta water, gently stir the pasta and swirl the pan until the sauce is incorporated, adding more pesto and pasta water until the sauce is creamy and smooth.
Store any leftover pesto in the refrigerator, covered with a thin layer of olive oil, for up to a week.