In a large pot, bring salted water to a boil. Cook the cheese tortellini according to package instructions, usually about 8-10 minutes, until al dente. Drain the tortellini in a colander and rinse under cold water to stop the cooking process. Set aside to cool.
In a mixing bowl, combine the halved cherry tomatoes, diced cucumber, diced bell pepper, chopped red onion, sliced black olives, and drained mozzarella balls.
In a separate small bowl, whisk together the olive oil, red wine vinegar, dried oregano, salt, and pepper until well combined.
Once the tortellini is cool, add it to the mixing bowl with the vegetables. Pour the dressing over the salad and gently toss everything together until well combined.
Adjust seasoning with additional salt and pepper if needed.
Chill the salad in the refrigerator for at least 15 minutes before serving to allow the flavors to meld.
Serve the salad garnished with fresh basil leaves if desired.