Cook the rotini pasta according to package instructions until al dente. Drain and rinse under cold water to cool.
In a large mixing bowl, combine the cooled pasta, cherry tomatoes, cucumber, red bell pepper, and red onion.
In a food processor, blend the fresh basil leaves, pesto sauce, and olive oil until smooth.
Pour the basil pesto mixture over the pasta and vegetables. Toss to combine thoroughly.
Add the grated Parmesan cheese, and season with salt and pepper to taste. Toss again to ensure everything is evenly coated.
Chill the pasta salad in the refrigerator for at least 30 minutes before serving to allow flavors to meld.