Steam or boil the swedes and potatoes together until tender, then drain well and mash. Beat in half the butter, season to taste with salt, pepper and nutmeg and spoon into an ovenproof dish. Melt the remaining butter in a frying pan, remove from the heat and stir in the breadcrumbs and the chopped parsley. Sprinkle the mixture over the mashed swede and potato and set aside.
When the turkey is removed from the oven, increase the temperature to 220°C. While making the gravy, put the gratin into the oven to cook until golden brown on top.