Bring a large pot of lightly salted water to a rolling boil. Cook the bow-tie pasta at a boil until tender yet firm to the bite, about 12 minutes; drain.
Quickly rinse the cooked pasta in cold water to stop it from continuing to cook; drain.
Mix the cooled pasta, broccoli, tomatoes, sliced green onions, celery, red bell pepper, and green bell pepper in a large bowl.
Gently stir the salad dressing, Parmesan cheese, sugar, basil, and salt in a bowl until evenly mixed.
Pour the salad dressing mixture over the pasta mixture; gently toss to coat evenly.