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Heat broiler to high. Wash and dry produce.
Dice potatoes into 1⁄2-inch pieces. Strip thyme leaves from stems; roughly chop leaves. Trim, peel, and halve carrot lengthwise; slice crosswise into 1⁄4-inch- thick half-moons. Finely dice celery. Halve, peel, and finely chop onion. Peel and mince garlic.