Cook the pasta according to package directions until al dente.
Drain and rinse with cold water to stop the cooking process.
While the pasta is cooking, make the pesto sauce. In a food processor or blender, combine the basil leaves, Parmesan cheese, pine nuts, garlic, and olive oil. Process until smooth, adding more olive oil if needed to achieve a smooth consistency. Season with salt and black pepper to taste.
In a large mixing bowl, combine the cooked pasta, cherry tomatoes, mozzarella cheese, and chopped parsley.
Pour the pesto sauce over the pasta mix, stirring to coat evenly.
Chill the pasta in the refrigerator for at least 30 minutes before serving.
Serve the pasta salad cold, garnished with additional Parmesan cheese and fresh basil leaves if desired.