Peel the potatoes and slice thinly on a mandoline or with a very sharp knife.
Heat the butter in a heavy-based frying pan that is about 8in (20cm) in diameter and about 2in (5cm) deep. Remove from the heat and cover the bottom with a layer of the potatoes.
Add a layer of onions over the potatoes and another of grated cheese, seasoning generously as you go. Continue these layers, finishing with a layer of potatoes and a sprinkling of cheese.
Cover tightly with tin foil and cook over a very low heat for 45 minutes to 1 hour until potatoes on top are just cooked through when pierced with a sharp knife.
Preheat the grill. Uncover the stoved potatoes and place straight under the grill to cook for 2-3 minutes until golden brown. Serve cut into slices, straight from the pan.