Put a chopstick or pencil along each long side of the potato so you don't cut through to the counter. Using a sharp knife, cut potatoes almost through cross-wise in 1/8” thick slices. Place in ice water to prevent darkening.
Drain well and put in shallow baking pan. Brush with butter (or drizzle).
Bake until tender- about 1-1/2 hours, basting occasionally with cream and pan drippings. Sprinkle with cheese in last few minutes.