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Adjust rack to top position and preheat oven to 425 degrees. Line a baking sheet with foil and brush with oil (or coat with nonstick spray). Wash and dry produce.
Trim and grate zucchini on the largest holes of a box grater. Place in the center of a clean kitchen towel. Gather into a tight bundle and squeeze over the sink to remove as much liquid as possible. (Alternatively, place in a fine-mesh strainer and press down with a spatula.)
Trim and thinly slice scallions, separating whites from greens. Drain corn, then pat dry with paper towels.