In a large bowl, combine the bread, corned beef and sauerkraut. In another bowl, whisk the eggs, cream and salad dressing; pour over bread mixture and toss to coat. Transfer to a greased 13x9-in. baking dish. Let stand 5 minutes.
Cover and bake at 375° for 40 minutes. Uncover; sprinkle with cheese and bake 5-10 minutes longer or until a knife inserted in the center comes out clean. Let stand for 10 minutes before cutting.