Melt the butter in a saucepan. Add the scraped, whole carrots, sugar, salt and enough stock to come half-way up the carrots. Cook gently, without a lid, shaking the pan occasionally until tender. Remove the carrots and keep them hot. Boil the stock rapidly until reduced to rich glaze. Replace the carrots 2 or 3 at a time, turn them until both sides are well coated with glaze. Dish, sprinkle with chopped parsley and serve.