1. Preheat oven to 450 degrees. Put garlic into an ovenproof ramekin, and drizzle with oil. Roast garlic until light brown and tender, about 20 minutes. Let stand until cool enough to handle. Peel garlic, cut into thin slices, and set aside. Reduce oven temperature to 425 degrees.

2. Melt 2 tablespoons butter in a 10-inch nonstick ovenproof skillet, swirling skillet to coat bottom and sides. Remove from heat. Starting at sides, arrange about half of the rutabaga slices, slightly overlapping, in a circular pattern, covering bottom; press. Sprinkle with 1/2 teaspoon salt, a pinch of pepper, 1/2 teaspoon thyme, and a third of the roasted garlic; dot with 1 tablespoon butter. Repeat process with potato slices, and then remaining rutabaga slices, for 2 more layers (do not sprinkle thyme on top layer).

3. Butter a large piece of foil with remaining tablespoon butter. Cover skillet tightly with foil, buttered side down. Place another skillet on top to weigh down. Bake until vegetables are tender, 50 to 60 minutes.

4. Transfer to a wire rack; let cool 15 minutes. Remove foil, and invert carefully onto a serving dish. Sprinkle with remaining 1/2 teaspoon thyme. Serve immediately, or refrigerate in an airtight container up to 1 day; reheat in a 300 degrees oven to serve.