Preheat oven to 350 degrees. Generously butter 13 x 9 inch casserole dish and then rub all over with garlic clove. Peel and thinly slice potatoes and parsnips. Arrange single layer of potatoes in dish. Season with sprinkling of thyme and salt and pepper. Cover with layer of sliced parsnips and top with about 1/3 layer of shredded cheese. Repeat layering process until all vegetables and cheese are used.
Pour cream over entire casserole. Cover and bake for additional 40 to 50 minutes, or until gratin is crisp and golden on top. Let stand a few minutes before serving. Serves 12.
