Cook the tortellini according to package instructions until al dente, then drain and let cool slightly.
In a medium bowl, whisk together the mayonnaise, Italian dressing, 1 tablespoon Parmesan, 1 tablespoon chopped parsley, and 1/2 teaspoon black pepper until smooth.
Prepare the vegetables: halve and thinly slice the cucumber, dice the red onion, finely chop both bell peppers, and halve the cherry tomatoes.
In a large serving bowl, combine the cooked tortellini and all prepared vegetables.
Fold the dressing into the tortellini and vegetables until evenly coated, stirring gently to avoid breaking the pasta.
Refrigerate the salad for at least 2 hours to chill and develop flavors.
Just before serving, garnish with additional chopped parsley and grated Parmesan.
