Heat oven to 400°F. Spray 12x8-inch (2-quart) glass baking dish with nonstick cooking spray.
Place bread cubes evenly in bottom of sprayed baking dish. Spread sauerkraut evenly over bread. Layer corned beef over sauerkraut. Pour dressing over corned beef. Spray sheet of foil with cooking spray; place, sprayed side down, over baking dish.
Bake at 400°F. for 20 minutes. Uncover; sprinkle with cheese. Bake, uncovered, an additional 5 to 10 minutes or until casserole is bubbly and cheese is melted.