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Adjust rack to top position and preheat oven to 425 degrees. Wash and dry all produce.
Peel and grate or mince ginger. Trim, peel, and cut carrot on a diagonal into ½-inch-thick pieces. Halve, core, and thinly slice bell pepper crosswise into strips. Halve, peel, and cut shallot into ½-inch-thick wedges. Zest and quarter lime.