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Adjust racks to top and middle positions and preheat oven to 425 degrees. Wash and dry produce.
Cut potatoes into ½-inch-thick wedges. Pick and roughly chop fronds from dill. Trim and halve zucchini lengthwise; slice crosswise into ½-inch-thick half-moons. Halve and peel onion; slice into ½-inch-thick wedges.
Cut broccoli into bite-size pieces or trim green beans if necessary. (Save potatoes for another use.)