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Adjust racks to top and middle positions and preheat oven to 450 degrees. Wash and dry produce.
Dice potatoes into 1⁄2-inch pieces. Trim, peel, and cut carrots on a diagonal into 1⁄2-inch-thick pieces. Strip thyme leaves from stems; chop leaves until you have 2 tsp (4 tsp for 4 servings). Halve, peel, and finely chop shallot.