Preheat the oven to 350 F and lightly butter three 4-inch springform mini cake pans.
In a large bowl (or stand mixer), mash the banana and whisk in the eggs, coconut oil, coconut milk and vanilla until smooth.
In a separate small bowl, add in all the dry ingredients (except for the grated carrot) and stir to combine.
Slowly add the dry mixture to the wet a little bit at a time, just until there is no raw flour visible and stopping to scrape down sides of the bowl. Make sure not to over mix, and then fold in the grated carrot.
Divide the batter evenly between your prepared cake pans.
Transfer the filled cake pans to a large baking sheet and bake for 35 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Transfer the baked mini cakes to a cooling rack to cool for 5 minutes, or until cool enough to touch. Remove the cake from the spring forms and place it directly on a rack to cool completely before frosting.
Once cooled you can add frosting as desired (see directions below). I added mine to the middle layers and on top with sprinkles for a complete naked cake look. You can cover it completely or style it as a semi-naked cake with scraped sides to expose some cake beneath the frosting.
The finished cake can be stored in an airtight container in the fridge for 2 days or in the freezer for 1 month.