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Put the beets into a small baking dish and rub them with 1 tablespoon of oil. Cover the dish with foil and put into the oven for 30 minutes.
In the meantime, peel and cut the carrots into 1-inch pieces, trim the Brussels sprouts and halve them lengthwise, and peel the garlic cloves. Put the carrots, Brussels sprouts and garlic cloves into a large baking dish and toss with the remainder of the oil. Sprinkle with salt and pepper.
After the beets have been cooking for 30 minutes add the large pan of vegetables to the oven and cook everything for 1 hour more, stirring the vegetable mixture once or twice.
Remove the beets from the oven and transfer them to a cutting board to cool. Stir the thyme into the carrot and Brussels sprouts mixture and let it continue to cook for another 10 minutes while the beets are cooled and cut. When the beets are cool enough to handle, about 5 minutes, peel them and cut them into 1-inch pieces. Remove the other vegetables from the oven, toss with the beets, season with salt and pepper, to taste, and serve.