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Preheat broiler to high (or preheat oven to 500 degrees). Wash and dry all produce. Cut one zucchini into ½-inch-thick rounds. Trim ends from remaining zucchini, then grate into a medium bowl using the large holes on a box grater. Trim, then thinly slice scallions, separating whites from greens. Pick oregano leaves from stems; discard stems and roughly chop leaves.