Preheat the oven to 425F°. Spray a baking sheet with cooking spray.
Fill a small bowl with egg whites, whisking well.
Fill another bowl with the breadcrumbs and Parmesan cheese, mix to combine.
Using a 1/3 cup measuring cup, form potatoes into 8 patties.
Brush patties with egg whites (or you can use your hands to spread egg on), then dip into breadcrumb mixture. Place patties onto the baking sheet and spray the top with more cooking spray.
Bake for 15 minutes, or until the bottom becomes golden brown; flip and cook an additional 10-12 minutes, until golden on both sides.