Preheat oven to 350 degrees F. Grease a 9x13 pan and set aside.
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cardamom, and cinnamon. Set aside.
In a large mixing bowl, add the mashed bananas, granulated sugar, brown sugar, egg, sour cream, vegetable oil, and vanilla extract. Using stand mixer, mix until well combined for 1-2 minutes. Add in the flour mixture and mix for 1-2 more minutes.
Place the zucchini on a paper towel and squeeze the liquid out of it; add it to the batter.
Pour the batter into cake pan. Sprinkle top with turbinado sugar (optional, especially if you choose to add frosting). Bake for 45-50 minutes, until a toothpick comes out clean when placed in the center. Cool on a wire rack for 20-30 minutes before frosting.
For frosting, combine brown sugar, butter and milk in a large saucepan. Bring to a boil over medium heat; cook and stir until thickened, 1-2 minutes. Remove from heat; stir in maple extract. Cool to lukewarm.
Gradually beat in confectioners’ sugar until frosting reaches spreading consistency. Frost the cake.
Store the cake covered with plastic wrap on the counter for up to 3 days. The cake also freezes well; freeze before frosting. Completely defrost before frosting.