Place zucchini in a long, glass or otherwise non-reactive pan. Pour dressing over zucchini and turn to make sure evenly coated. Cover and all to marinate for 30 minutes to a few hours.
Heat grill to 350ยบ F. Place zucchini slices onto grill and cook about 5 minutes. Flip to grill the other side of the zucchini and cook until fork tender, about 5 more minutes.
Remove from grill with tongs and keep warm until serving. If serving with Parmesan cheese, sprinkle on top while still warm.