Preheat oven to 400°. Butter a 9- by 13-in. baking dish with 1 tbsp. butter. Arrange a third of the sweet potatoes, overlapping slightly, in the dish. Sprinkle with 1/4 cup cheese. Repeat with two more layers of sweet potatoes and cheese.
In a small bowl, combine cream, salt, pepper, and cayenne. Pour over potatoes. Dot with the remaining 2 tbsp. butter. Cover dish with foil and bake 20 minutes. Remove foil and continue baking until sweet potatoes are tender and top is browned, 20 to 25 minutes.
Note: Nutritional analysis is per serving.