Cook the pasta according to package instructions in a large pot of salted boiling water until al dente. Drain and set aside, reserving 1/2 cup of the pasta cooking water.
In a food processor, combine the basil leaves, Parmesan cheese, pine nuts, and minced garlic. Pulse until finely chopped.
With the food processor running, slowly drizzle in the olive oil until the mixture is smooth and creamy. Season with salt and pepper to taste.
In a large mixing bowl, combine the cooked pasta, pesto, and reserved pasta water. Toss until the pasta is well coated.
Gently fold in the cherry tomatoes and mozzarella balls.
Serve immediately, garnished with extra basil leaves.