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Adjust rack to top and middle positions and preheat oven to 450 degrees. Cut 1 TBSP butter (2 TBSP for 4 servings) into four cubes (eight cubes for 4). Place butter in a small bowl; bring to room temperature. Wash and dry produce.
Trim, peel, and cut carrots into sticks (like fries—ours were 3 inches long and 1⁄3 inch thick). Thinly slice tomato into rounds.
Cut broccoli florets into bite-size pieces if necessary. (Save carrots for another use.)