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Adjust rack to top position and preheat oven to 425 degrees. Wash and dry produce.
Trim and thinly slice cucumber crosswise into rounds. Trim, peel, and grate carrot on the largest holes of a box grater. Roughly chop cilantro. Halve lime. Halve, peel, and thinly slice shallot. Cut potatoes into ½-inch-thick wedges. Peel and mince ginger.