Preheat the oven to 425F (see notes at the end).
Wash and scrub the potatoes. Pat dry with paper towels.
Slice the potatoes without going all the way through — i.e., the slices should still be attached at the bottom so that each potato is still effectively in one piece.
Place the potatoes on a shallow baking pan. Brush some of the melted butter over them. Sprinkle with salt and pepper. Roast for 40 minutes.
Take the potatoes out of the oven (they would have opened up at this point). Brush the softened butter between the slices then drizzle the remaining butter over them. Return to the oven and roast for another 10 minutes.
Remove the potatoes from the baking pan with a spatula. Drizzle with more butter, if you like. Serve hot.