Preheat the oven to 350°.
Grease or spray an 8x8-inch square pan then line it with parchment paper.
FOR THE CAKE: In a large bowl, mix the flour, sugar, cinnamon, baking powder, baking soda, and salt. Set aside.
In another small bowl mix the egg, oil, and vanilla extract. Then mix in the bananas, Then mix in the zucchini. Add this mixture to the dry ingredients.
Spread the batter evenly into the prepared pan.
Bake at 350° for 35-40 minutes or until a cake tester inserted in the middle comes out clean.
Cool the cake in the pan on a wire rack for an hour, then remove parchment paper and place the cake on a flat surface to frost it and then cut into squares.
FOR THE FROSTING: With a mixer on medium speed, beat all the frosting ingredients until smooth. Spread the frosting on top of the cake. Optional: Sprinkle chopped nuts on top. Cut the cake into 16 squares.
Cover and store the cake squares in the refrigerator.