Brush the bottom of a 9-inch heavy oven-proof non-stick or well-seasoned cast-iron skillet with 1 tablespoon of the butter. Peel 1 potato, slice it thin, using a food processor fitted with the slicing blade, or a mandoline or similar slicing device, and pat the slices dry quickly. Arrange the slices, overlapping them slightly, in layers in the skillet, brushing each layer with some of the remaining 3 tablespoons butter and seasoning it with salt and pepper. Peel, slice, pat dry, and arrange the remaining potatoes, 1 at a time, in the same manner. Cover the layered potatoes with foil, weight them with an ovenproof saucepan, and cook them over moderate heat for 5 minutes from the time the butter sizzles. Transfer the skillet with the pan weight to the middle of a preheated 425°F. oven and bake the potatoes for 30 minutes. Remove the weight and the foil and bake the potatoes, for 10 minutes more, or until they are tender. The potatoes may be made 2 hours in advance and kept, covered loosely, at room temperature. Reheat the potatoes, covered with the foil, in a preheated 375°F. oven for 15 minutes.