Bring a large pot of salted water to a boil. Add the gemelli pasta and cook until al dente according to package directions. Drain the pasta in a colander and rinse briefly under cool water to stop the cooking.

While the pasta cooks, place the pine nuts in a small dry skillet over medium heat. Toast them for 3 to 4 minutes, shaking the pan often, until they turn light golden. Remove from heat and set aside.

In a large mixing bowl, combine the basil pesto and olive oil. Stir until the pesto loosens slightly and becomes easier to coat the pasta.

Add the cooled gemelli to the bowl with the pesto. Toss until every piece is evenly coated.

Fold in the halved cherry tomatoes, toasted pine nuts, and grated Parmesan cheese. Season with salt and black pepper to taste, then toss once more.