Preheat oven to 425°. Brush bottom and sides of a 9-inch oven-safe nonstick skillet with about 1 tablespoon melted butter.
Peel potatoes. Using a mandoline, food processor, or sharp knife, slice potatoes into 1/8-inch-thick disks. Pat dry with paper towels; then quickly arrange slices in overlapping circular layers in pan. Brush each layer with butter and season with salt and pepper to taste. Gently push potatoes down with a plate for a snug fit.
Remove plate; cover potatoes with foil and bake 20 minutes. Remove foil and bake until potatoes are easily pierced with a fork and golden, 30-35 minutes more.
Place a small cutting board or serving plate on top of pan. With oven mitts on, invert potato cake onto board or plate. Let rest 5 minutes before serving.