Arrange 6 slices bread in a greased 13×9-in. baking dish. Combine eggs, milk, 1/3 cup sugar and vanilla; pour half over bread. Top with apples. Combine cinnamon, nutmeg and remaining 1/3 cup sugar; sprinkle over apples. Top with remaining slices bread; pour remaining egg mixture over bread. Dot with butter. Cover and refrigerate 8 hours or overnight.
Remove from refrigerator 30 minutes before baking. Preheat oven to 350°. Bake, uncovered, until a knife inserted in center comes out clean, 45-50 minutes. Let stand 5 minutes before serving. If desired, serve with whipped cream and syrup.