1. Preheat oven to 350°. Stir together onions, hash browns, and cheese in a very large bowl. Whisk together soup and remaining ingredients in another bowl until blended. Pour over potato mixture, stirring to coat.
2. Spoon potato mixture into a greased 13- x 9-inch baking dish. Bake, uncovered, at 350° for 1 hour and 15 minutes or until browned.
Substitute shredded Italian cheese for one of the packages of shredded Cheddar for depth.