Place bread cubes in a 13x9-in. baking dish coated with cooking spray; set aside.
In a large skillet, saute mushrooms and onion in oil until tender. Add garlic; cook 1 minute longer. In a large bowl, combine the eggs, egg whites, milk, spinach, cheeses, mustard, salt, nutmeg, pepper and mushroom mixture; pour over top. Cover and refrigerate overnight.
Remove from the refrigerator 30 minutes before baking. Bake, uncovered, at 350° for 50-60 minutes or until a knife inserted in the center comes out clean. Let stand for 10 minutes before cutting.