Fill a large pot with lightly salted water and bring to a rolling boil; stir in tortellini and return to a boil. Cook uncovered, stirring occasionally, until the tortellini float to the top and the filling is hot, about 3 minutes. Be sure not to overcook, as they’ll start to unfold. Drain well, cool to room temperature, and transfer to a large bowl.

Combine tomatoes, mozzarella balls, cucumber, bell peppers, pepperoni, banana peppers, red onion, black olives, parsley, salt, and pepper in a separate bowl, and add to the tortellini.

Drizzle Italian dressing over salad, lightly tossing all ingredients until well coated. Refrigerate for at least 1 hour before serving.