Combine hash browns and next 4 ingredients in a large bowl.
Stir together milk and next 5 ingredients; pour over hash brown mixture. Pour into a lightly greased 13- x 9-inch baking dish.
Bake at 350° for 45 to 55 minutes or until golden.
Pepper Jack-Potato Casserole: Omit colby-Jack and Swiss cheeses, onion, and beef broth. Substitute 1 (8-ounce) package Monterey Jack cheese with peppers, shredded. Proceed as directed. Bake at 350° for 45 to 50 minutes or until bubbly.