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Adjust rack to top position and preheat oven to 425 degrees. Wash and dry produce.
Quarter zucchini lengthwise; slice crosswise into 1⁄2-inch-thick pieces. Trim, peel, and cut carrots on a diagonal into 1⁄4-inch-thick pieces (halve lengthwise first if carrots are on the larger side).
Toss zucchini and carrots on a baking sheet with a large drizzle of olive oil, half the Za’atar Spice (all for 4 servings), salt, and pepper. (TIP: For easy cleanup, line sheet with aluminum foil first.) Roast on top rack until browned and tender, 18-22 minutes.