Preheat oven to 350 degrees F. Grease a 9-10″ cake pan with coconut oil or cooking spray.
In a medium bowl, combine your dry ingredients: flour, baking powder, baking soda, salt, and cinnamon. Set aside.
In a large bowl, whisk together the brown sugar, oil, eggs, and vanilla. Stir in the zucchini and mashed bananas. Add the dry ingredients until just combined.
Pour batter into the prepared pan and bake until a toothpick inserted in middle comes out clean (about an hour). Turn out onto wire rack and allow the cake to completely cool.
Icing
In the bowl of a stand mixer, or with a hand mixer, cream together butter and cream cheese until smooth. Add vanilla and sugar and beat until creamy. Spread icing on top of cooled cake.