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Adjust rack to top position (top and middle positions for 4 servings) and preheat oven to 425 degrees. Bring a large pot of salted water to a boil. Wash and dry produce.
Trim and halve zucchini lengthwise; slice crosswise into 1⁄2-inch-thick half-moons. TIP: If you added any other items to your meal (apps, sides, and/or dessert), you can get started on them now!
Adjust rack to top and middle positions. Cut broccoli into bite-size pieces if necessary. Toss on a baking sheet with a drizzle of oil, salt, and pepper. Roast on middle rack until browned and tender, 15-20 minutes.