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Adjust racks to top and middle positions and preheat oven to 425 degrees. Wash and dry all produce.
Cut potatoes into ½-inch-thick wedges. Halve and peel shallot. Grate one half on the largest holes of a box grater; place in a large bowl. Mince remaining shallot. Peel and mince garlic. Strip thyme leaves from stems; roughly chop leaves.