Boil the cabbage and potatoes in separate saucepans in plenty of slightly salted water. Cook the cabbage for about five minutes until tender but still crisp. Drain well, rinse in cold water, drain again and squeeze out any excess water with your hands. Pat dry on kitchen paper.
Cook the potatoes for three minutes, then drain, place in cold water, drain again and dry well on kitchen paper.
Grease an ovenproof dish generously with some of the butter.
Arrange half of the potato slices, slightly overlapping, on the bottom of the dish, dot with some more butter and season with salt and pepper.
Arrange the cabbage and half of the cheese on top of the potatoes, and season with salt and pepper. Top with the remaining potatoes and cheese. Dot with the remaining butter.
Cover with foil and bake for 25 minutes, removing the foil five minutes before the end of the cooking time. Remove from the oven and serve.