Toast the pine nuts in a dry skillet over medium heat until golden and fragrant, about 3 minutes. Transfer to a bowl and let cool.

In a food processor, combine the toasted pine nuts, basil, garlic, Parmesan, olive oil, lemon juice, salt, and pepper. Pulse until nearly smooth but still with small flecks of basil, about 30 seconds.

Cook the penne in a large pot of salted boiling water until al dente, 9 to 11 minutes. Reserve ½ cup pasta water, then drain.

Return the hot pasta to the pot off the heat. Add the pesto and 2 tablespoons reserved pasta water and toss until evenly coated. Serve with extra Parmesan.