Bring a large pot of salted water to a boil. Toast the pine nuts in a dry skillet over medium heat until golden, 3 to 4 minutes. In a food processor, blend the basil, pine nuts, garlic, and Parmesan. With the motor running, drizzle in the olive oil until smooth. Season with salt and pepper.

Cook the pasta in the boiling water until al dente, about 8 to 10 minutes. Drain, rinse under cold water, and spread on a baking sheet to cool.

In a large bowl, toss the cooled pasta with the pesto, cherry tomatoes, and mozzarella. Add a splash of olive oil or water if needed to loosen the sauce.

Transfer to a serving dish. Top with toasted pine nuts, fresh basil, and extra Parmesan. Serve at room temperature or chilled.