Slice zucchini into pieces, about 1/2" wide and 3-4" long.
In a small bowl, beat egg whites and season with salt and pepper. In a ziplock bag, place breadcrumbs, garlic powder and cheese and shake well. Spray cookie sheet with cooking spray and set aside.
Dip zucchini sticks into eggs then into bread crumb and cheese mixture, a few at a time and shake to coat. Place the breaded zucchini in a single layer and spray more cooking spray on top. Bake at 425° for about 20-25 minutes, or until golden brown.