Place carrots and potatoes into a large pot and cover with salted water. Bring to a boil over high heat, then reduce heat to medium-low, cover, and simmer until tender, about 20 minutes. Drain and allow to steam dry for a minute or two.
Meanwhile, melt the butter in a small saucepan over medium heat, then stir in the applesauce and brown sugar until dissolved. When the potatoes are ready, transfer to a serving bowl and mash until smooth. Then fold in the applesauce mixture and raisins.
