Preheat oven to 425 F. Slice off a portion of the bottom lengthwise to create a flat bottom, which will make slicing easier. Place potato flat side down between two chopsticks or skewers and slice each potato crosswise at 1/8-inch intervals, cutting to within 1/4 inch of the bottom. The chopsticks or skewers will prevent cutting through.
Arrange potatoes spoke-fashion in a buttered 10-inch pie dish. Drizzle 2 tablespoons melted butter evenly over potatoes, and sprinkle with salt.
Bake potatoes at 425 F on middle oven rack for 30 minutes. Sprinkle breadcrumbs over potatoes, drizzle with remaining melted butter and bake 20 more minutes.
Sprinkle cheese over potatoes, baste with butter in pan and bake five more minutes or until potatoes are golden.