Butter the sides and bottom of a 30 x 20-cm (12 x 8-inch) baking dish. Line the bottom of the dish with parsnip slices. Sprinkle with cheese and drizzle with cream. Season with salt and pepper. Cover with a layer of carrots, drizzle again with cream and sprinkle with cheese. Continue with the remaining ingredients. Season with salt and pepper between each layer. Cover with aluminum foil.