Heat half the butter in the skillet with 3 of the sage leaves, left whole. Roughly chop or tear the rest of the leaves. Cover the bottom of the skillet thoroughly with 2 overlapping layers of potatoes. Season with salt and pepper to taste and cover with a portion of the cheese. Continue layering the potatoes and cheese, seasoning each layer with salt and pepper. Finish with a layer of potatoes.

Tightly cover the pan with foil. Set over low heat and cook for about 40 minutes or until the potatoes are tender when pierced with a knife. Loosen the bottom layer with a spatula, invert the cake onto a plate, and add the rest of the butter to the pan. Slide the cake back in and continue cooking until the bottom layer is lightly browned, another 15 minutes or so. Turn out of the pan and serve.