Preheat oven to 425°.
Place the flour in a medium saucepan. Gradually add the milk, stirring with a whisk until blended. Stir in cider, broth, salt, pepper, and nutmeg; bring to a boil over medium heat, stirring constantly. Remove from heat. Combine cheeses in a small bowl. Arrange half of the potato slices in a shallow 3-quart casserole, and sprinkle with 1/2 cup cheese mixture. Arrange the remaining potato slices on top. Pour the cider mixture over the potatoes, and bake at 425° for 25 minutes. Remove from oven; press potatoes with a spatula. Sprinkle with 1/2 cup cheese mixture, and bake an additional 20 minutes or until potatoes are tender. Let stand 10 minutes.