Preheat the oven to 350 degrees . Grease two 12-cup muffin pans. In a large bowl, mix together the mashed bananas, carrot, egg and honey; stir in 3 cups water.
In another large bowl, stir together the flour, cinnamon, allspice, ginger and baking powder; mix into the carrot mixture.
Fill each muffin cup about three-quarters full. Bake until firm and dry, about 45 minutes. Let cool, then top each cupcake with more grated carrot and smear with cream cheese.