Toast pine nuts in a dry skillet over medium-low heat, shaking often, until golden and fragrant, 2 to 3 minutes. Let cool.

In a food processor, combine basil, pine nuts, garlic, Parmesan, lemon juice, and 1/2 tsp salt. Pulse until chopped, then drizzle in olive oil with the motor running until smooth.

Cook pasta in heavily salted boiling water until al dente, 8 to 10 minutes. Reserve 1 cup pasta water, then drain.

Return pasta to the pot and add the pesto with 1/4 cup reserved pasta water. Toss until creamy, adding more water as needed. Serve hot with extra Parmesan and basil.