Cook tortellini according to package directions; drain and rinse under cold running water. Place pasta in large colander bowl and set aside.
Meanwhile, slice zucchini, chop carrot, cut cherry tomatoes in half, thinly slice green onions and snip parsley.
Add vegetables to tortellini. Pour salad dressing over salad. Grate Parmesan cheese over salad; mix gently. Cover; refrigerate at least 2 hours before serving.