- With the rack in the middle position, preheat the oven to 180 °C (350 °F).
- With a mandolin, thinly slice the parsnips and carrots lengthwise.
- In a bowl, combine the cream and garlic.
- 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.
- Bake for about 2 hours. Remove the foil and continue cooking for 20 minutes or until the vegetables are tender. Brown under the broiler if desired.
- Let stand for 10 minutes, cut into squares and serve.