In a large pot, bring salted water to a rolling boil. Add the cheese tortellini and cook according to the package instructions or until they are tender but still firm to the bite (al dente). Once cooked, drain the tortellini and immediately rinse them under cold water to halt the cooking process and cool them down.
In a spacious mixing bowl, combine the halved cherry tomatoes, diced cucumber, diced bell pepper, finely chopped red onion, and sliced black olives. Stir gently to ensure the vegetables are evenly mixed.
Carefully add the cooled tortellini to the bowl of vegetables. Use a spatula to gently toss the mixture until the tortellini and vegetables are well combined without breaking the tortellini.
Drizzle the Italian dressing over the entire salad, then add the freshly chopped basil, along with salt and freshly cracked pepper to taste. Toss everything together with care so that the dressing coats all the ingredients uniformly.
Cover the salad with plastic wrap or a lid and place it in the refrigerator. Allow it to chill for a minimum of 30 minutes, letting the flavors meld and intensify.
Before serving, give the salad a gentle final toss to redistribute the dressing, then transfer to a serving dish. Garnish with a generous sprinkle of grated Parmesan cheese for an added burst of flavor.