Roasting carrots concentrates the sugar in the root by evaporating the moisture and creating a crispy exterior skin with a soft marsh-mallowy texture inside. And speaking of marshmallows, if you let the carrots burn a bit, they taste remarkably like smoky-sweet burnt marshmallows. Leave the carrots in large pieces or even whole to give them enough time to roast thoroughly.
I rarely grill root vegetables, but in the summer, when turning on the oven in an already hot house feels like a mortal sin, wrapping the roots in foil and letting them roast on the grill will yield a similar result with a slightly smoky flavor.