Preheat the oven to 180C/350F/Gas 4.
Cook the potatoes and swede in a saucepan of salted boiling water until tender. Drain well and return to the pan.
Heat 50g/2oz butter in a pan and gently cook the cabbage for a few minutes, until the cabbage is tender but retains its colour.
Add the cabbage to the pan with the potatoes and swede. Add the remaining 25g/1oz butter and mash together using a potato masher. Season, to taste, with salt and freshly ground black pepper.
Place the mashed vegetables into an ovenproof lidded dish and top with the cheese.
Cover with a lid and bake in the oven for about 30 minutes, then remove the lid and continue to cook for a further 15 minutes, or until piping hot and golden-brown on top.