1. Preheat the oven to 350u. Place the sweet potatoes on a piece of aluminum foil and roast until they can be easily pierced with a fork, about 1 hour. Let cool slightly.
2. Trim the ends and pull off the peels; slice into 1/2-inch rounds.
3. Butter a small (31/2-quart) casserole dish with half the butter. In a bowl, stir together the cinnamon, ginger and allspice. Arrange half the apple rings and sweet-potato rounds in alternating layers in the dish; sprinkle with half the spice mixture and half the maple syrup. Layer in the rest of the apples and sweet potatoes, ending with the apples. Sprinkle with the remaining spices, drizzle with the remaining syrup; dot with the rest of the butter.
4. Cover and bake until the apples are very tender, about 45 minutes.