Use true baby carrots, which are sweet and tender, instead of shaved-down regular carrots.
Preheat oven to 450°.
Place 1 oven rack in upper third of oven, and place the second rack in lower third of oven.
Cut tops off carrots; discard tops. Combine carrots and remaining ingredients except cooking spray in a large bowl; toss to combine. Divide vegetable mixture evenly between 2 jelly-roll pans coated with cooking spray. Bake at 450° for 12 minutes, stirring once; rotate pans on oven racks. Bake 12 additional minutes or until vegetables begin to brown, stirring once.