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Adjust rack to top position and preheat oven to 425 degrees. Wash and dry produce.
Strip half the thyme leaves from stems (all the leaves for 4 servings); mince leaves. Trim, peel, and finely dice carrots. Finely dice celery. Halve, peel, and dice half the onion (whole onion for 4). Peel and mince garlic.