Trim crusts from bread. Arrange half of the bread in a 13 x 9-inch baking dish coated with cooking spray.
Combine milk, 1 1/2 cups egg substitute, half-and-half, and 1/2 cup sugar in a large bowl, stirring with a whisk. Pour half of milk mixture over bread in dish.
Combine 1/2 cup egg substitute, 1/2 cup sugar, vanilla, nutmeg, and cheeses in a food processor or blender; process until smooth. Pour cream cheese mixture over moist bread in dish. Top with remaining bread; pour remaining milk mixture over bread. Cover and refrigerate 8 hours or overnight.
Preheat oven to 350°.
Uncover and bake at 350° for 55 minutes. Let stand 10 minutes before serving. Sprinkle with cinnamon-sugar, if desired.