Bring a large pot of salted water to a boil and cook the tortellini according to the package instructions. Drain and rinse under cold water to stop the cooking.
In a large mixing bowl, combine cooked tortellini, cherry tomatoes, red onion, and Parmesan cheese.
Add pesto and olive oil, then toss gently to coat everything evenly.
Season with salt and pepper to taste.
Chill in the fridge for at least 30 minutes before serving.
Garnish with fresh basil if desired and serve cold or at room temperature.