Preheat oven to 400°.
Place bread cubes in a single layer on a jelly-roll pan. Bake at 400° for 8 minutes or until toasted. Increase oven temperature to 450°. Combine first 6 ingredients in a bowl; stir well. Set aside.
Coat an 8-inch nonstick skillet with cooking spray, and place over medium heat until hot. Add chopped red onion and garlic, and sauté 3 minutes. Add mushrooms, and sauté 5 minutes. Stir in bread cube mixture, and spread evenly in bottom of skillet. Cook over medium-low heat 5 minutes or until almost set.
Wrap handle of skillet with foil; place skillet in oven, and bake at 450° for 5 minutes or until set. Sprinkle with cheese; bake an additional minute or until cheese is warm (cheese will not melt).
Note: Substitute 1 cup egg substitute for 6 egg whites and 1 egg yolk, if desired.