Preheat the oven to 350°F (175°C). Grease and flour a 9×9-inch square baking pan or line it with parchment paper.
In a medium bowl, whisk together the all-purpose flour, baking soda, baking powder, ground cinnamon, and salt. Set aside.
In a large bowl, combine the granulated sugar, light brown sugar, and vegetable oil. Beat in the eggs one at a time, then stir in 1 teaspoon vanilla extract until well combined.
Add the shredded zucchini and mashed bananas to the wet ingredients and mix until evenly incorporated.
Gradually add the dry ingredients to the wet ingredients, stirring just until combined. Do not overmix.
If using, fold in the chopped walnuts gently.
Pour the batter into the prepared baking pan and spread it evenly.
Bake for 40 to 45 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool completely in the pan on a wire rack before frosting.
To prepare the whipped cream cheese frosting, beat the softened cream cheese and unsalted butter together in a large bowl until smooth and creamy.
Add the sifted powdered sugar and 1 teaspoon vanilla extract and beat until combined.
In a separate chilled bowl, whip the cold heavy whipping cream until stiff peaks form.
Gently fold the whipped cream into the cream cheese mixture until fully incorporated and smooth.
Spread the whipped cream cheese frosting evenly over the cooled cake.
Slice and serve. Store any leftovers covered in the refrigerator.