Peel and chop the potatoes and turnips and boil them togethr in a large pan of salted water for 25 to 30 minutes until tender.
Preheat the oven to 325*F.
Drain the vegetables well, return them to the pan and cover tightly, then shake over a low heat to dry them off completely.
Heat half the butter in another pan, add the cabbage and cook until just tender, but still bright green (about 3 to 4 minutes) Tip all the buttery cabbage into the potato pan and add the remaining butter.
Roughly mash everything together and season to taste with salt and pepper.
Tip into an ovenproof dish, top with cheese and bake for 30 minutes.
Before serving, preheat the grill and flash under the grill for 5 minutes to brown the top.