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Adjust racks to top and middle positions and preheat oven to 425 degrees. Wash and dry all produce. Halve and peel shallot. Grate one half on the largest holes of a box grater; place in a medium bowl (use a large bowl for 4 servings). Mince remaining shallot. Mince garlic. Strip thyme leaves from stems; roughly chop leaves and discard stems. Halve carrots lengthwise. Cut potato into ½-inch-thick wedges.