Preheat oven to 350°F. Cook bacon in large skillet until crisp. Drain bacon on paper towels; crumble and set aside. Remove all but 2 tablespoons drippings from skillet. Add onion to skillet; cook and and stir 3 minutes or until softened.
Spread 1/2 of the bread cubes in 13x9-inch baking dish. Layer with 1/2 each of the onion, bacon, Cheddar cheese and mozzarella cheese. Spread evenly with cottage cheese. Top with remaining bread cubes, onion, bacon, Cheddar cheese and mozzarella cheese.
Beat eggs in medium bowl with wire whisk. Add milk, mustard, pepper and nutmeg; mix well. Gradually pour into baking dish. Press bread cubes lightly into egg mixture until completely covered. Let stand 10 minutes.
Bake 40 to 50 minutes or until center is set and top is golden brown.