Preheat oven to 350 degrees F. Line and butter two 9-inch round cake tins.
In a bowl, mix together banana, mayonnaise, vanilla, and sugar until well combined.
In another bowl whisk together all purpose flour and baking soda.
Add flour mixture to mayonnaise mixture, and gently mix until no streaks of flour can be seen. Then fold in chocolate chips to distribute.
Divide batter into prepared tins, and spread out evenly. Bake for 45 minutes.
Allow to cool, and remove from tin.
Whisk all ingredients for frosting until light and fluffy.
Frost bottom layer of cake with half the frosting, and top with top layer of cake. Frost top layer with remaining frosting, and garnish with additional chocolate chips. Slice and enjoy!