Slice the peeled potatoes into rounds about 1/16 inch thick (slicing on a mandolin is easiest).

Generously butter a 6-inch round cake pan and arrange a layer of potatoes in a circle over the base, neatly overlapping each slice. Drizzle with a little of the melted butter, sprinkle with some of the Parmesan, and season with salt and pepper. Continue layering, drizzling with butter, sprinkling with cheese, and seasoning, until all the potatoes have been used.

Drizzle the remaining butter over the top and bake in a preheated oven at 425°F for about 40 to 50 minutes or until very tender. Press down the potato slices 3 or 4 times during baking to form a solid cake.