Use a well-seasoned cast-iron skillet or a heavy nonstick pan, and be careful when turning this golden potato cake.
In a well-seasoned large, heavy skillet, melt over low heat:
3 tablespoons butter
Pour out and reserve all but 1 tablespoon of the butter. Arrange in concentric circles in the skillet:
1 1/2 pounds baking potatoes, peeled and thinly sliced
As you build layers, sprinkle them with the reserved melted butter and season with:
Salt and ground black pepper to taste
Cover tightly and cook until the potatoes are golden on the bottom, 20 to 25 minutes. Turn the cake out onto a plate, then slide it back into the pan to brown the second side, about 15 minutes. Pierce with a knife to make sure the slices are tender all the way through. If not, continue to cook over low heat for 5 minutes more.
