Peel potatoes and cut into 1/8- to 1/4-inch-thick slices. Put the slices in a casserole (11- to 12-cup size, about 10 in. wide and 2 in. deep); shake to settle the potatoes down into the container.
Mix the broth, ground nutmeg, and pepper. Pour the mixture over potatoes.
Bake in a 425° oven until potatoes are very tender when pierced, 1 hour to 1 hour and 15 minutes. As potatoes get dry on top, tilt casserole and spoon up some of the broth to baste them.
Sprinkle potatoes evenly with cheese. Bake until it melts, about 3 minutes.
Let casserole sit 5 to 10 minutes for most of the remaining juices to soak into potatoes, then serve.