Preheat the oven to 350 degrees F.
In a medium size bowl, add the flour, baking powder, baking soda, salt and cinnamon. Mix together and set aside.
In a large mixing bowl, add the butter and sugar. Beat together. Add the eggs and beat until light and fluffy.
Turn the mixer speed to low and using a spoon, add the dry ingredients little by little. Mix until the flour is incorporated.
To the bowl, add mashed bananas and shredded carrots. Use a large sturdy spoon to mix the bananas and carrots in the batter.
Grease the doughnut baking pan with butter. Add the batter evenly to the pan.
Bake in a preheated oven until a wooden toothpick inserted in the doughnuts comes out clean (about 17 minutes).
Remove the doughnuts from the oven and let cool just long enough so that the doughnuts can be removed by hand and transferred to a cooling rack.
When the doughnuts have cooled, top with cream cheese frosting. Garnish with a small piece of carrot (shaped like a whole carrot) and a small piece of curly parsley as the green “top” of the whole carrot.