Carrot Buns is what I used to buy and eat in my first professional job years ago. They were split and had butter and cheese in between. Actually quite popular. Funny to think that maybe they still sell them there. Why ditch a good product?
My mother also made carrot buns, but there were a bit more healthy. She used oat flakes and oat bran. They were quite heavy, but still very good. I grated the carrots rough, however, as she said to do.