Coat an omelet pan with cooking spray; heat over medium heat. Add zucchini to pan; cook, tossing frequently, until tender crisp, about 2 to 3 minutes. Remove zucchini from pan; set aside.
In a medium bowl, beat egg whites, egg, salt and pepper until frothy.
Off heat, coat pan with cooking spray again; heat over medium heat. Pour eggs into pan and tilt pan to cover entire surface evenly with eggs; cook until bottom is set, about 2 to 3 minutes.
Place zucchini on middle of eggs in pan; sprinkle with cheese and basil. Fold eggs over filling to form omelet and continue cooking until inside of omelet is just cooked, about 1 to 2 minutes more. Serve immediately. Yields 1 omelet per serving.