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Adjust rack to top position and preheat oven to 450 degrees. Wash and dry produce.
Trim, peel, and dice carrots into 1⁄2-inch pieces. Trim and halve zucchini lengthwise; slice crosswise into 1⁄2-inch-thick half-moons. Peel and mince or grate garlic.
Place carrots in a medium pot with enough salted water to cover by 2 inches. Bring to a boil and cook until very soft, 15-20 minutes. Drain and return carrots to pot. Keep covered off heat until ready to mash.