Cook the pasta according to package instructions until al dente. Drain and rinse under cold water to cool.
In a food processor, combine 1 cup fresh basil leaves, ⅓ cup grated Parmesan cheese, ⅓ cup olive oil, 2 tablespoons pine nuts, 1 clove garlic, ½ teaspoon salt, and ¼ teaspoon black pepper. Blend until smooth. If desired, add the juice of ½ a lemon for extra brightness and blend again.
In a large bowl, combine the cooled pasta, halved cherry tomatoes, fresh mozzarella, and torn basil leaves.
Pour the pesto dressing over the pasta mixture and toss gently until everything is well coated.
Taste and adjust seasoning if necessary. Serve immediately or chill in the refrigerator for 30 minutes to allow flavors to meld.