Process the basil, garlic and pine nuts together in a food processor. With the motor running, add the oil in a steady stream until mixed to a smooth paste. Transfer to a bowl, stir in the parmesan and season to taste.
Cook the pasta in a large saucepan of rapidly boiling salted water until al dente. Drain and return to the pan. Toss enough of the pesto through the pasta to coat it well. Serve sprinkled with parmesan.