Combine first 5 ingredients and 1/2 cup shredded Cheddar cheese; spoon mixture into a lightly greased 13- x 9-inch baking dish.
Bake at 350° for 40 minutes. Sprinkle with remaining 1/2 cup Cheddar cheese, and bake 5 more minutes.
For Hash Brown-Ham-Cheese Bake, stir in 2 cups chopped cooked ham.