Coat a large nonstick skillet with cooking spray. Place hash brown patties in skillet; cook over medium heat on first side until golden brown, about 7 to 9 minutes. Flip patties; cook until golden brown on second side, about 5 minutes more.
Meanwhile, coat a second large nonstick skillet with cooking spray; heat over medium-low heat. In a large bowl, beat together eggs, egg whites, bacon, scallion, hot pepper sauce, salt and pepper; pour into prepared skillet and then increase heat to medium. Let eggs partially set and then scramble using a spatula. When eggs are set, but slightly glossy, remove from heat; cover to keep warm until hash browns are finished cooking.
To assemble stacks, place 1 hash brown patty on each of 4 plates. Top each with 1/4 of egg mixture and serve with 2 teaspoons of ketchup. Season to taste with salt and pepper, if desired. Yields 1 stack per serving.