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Adjust racks to middle and top positions (middle, top, and bottom positions for 4 servings) and preheat oven to 425 degrees. Wash and dry produce.
Cut potatoes into ½-inch-thick wedges. Halve, peel, and mince shallot. Peel and mince or grate garlic. Finely chop parsley. Cut broccoli into bite-size pieces if necessary.