Preheat the oven to 400 degrees F.
Thinly slice the potatoes using a mandoline, the slicing blade of a food processor or a chef's knife.
Place the butter in the cast-iron or ovenproof skillet and melt it in the preheated oven. Remove and swirl the butter around to coat, and then pour the butter into a dish.
Arrange the sweet potato slices in overlapping concentric circles in the skillet, brushing each layer with some of the butter, sprinkling with salt and pepper, and pressing down to compact, until all of the potatoes and butter have been used. Place a layer of foil directly on the top layer and place an empty pan on top to pack the potatoes down.
Bake until the potato cake can be easily pierced with a knife indicating the potatoes are tender, about 45 minutes. Run a metal spatula around the edge and then carefully invert the potato cake onto a serving platter.