Make the Cake: Preheat oven to 350 degrees F. Spray a 9x9-inch baking pan with non-stick cooking spray.
In a small bowl, whisk together the flour, cocoa powder, baking salt and salt.
Using an electric mixer, beat the butter, both sugars, eggs and vanilla on medium speed until smooth and creamy, 2 to 3 minutes.
Reduce the mixer speed to low, add one-third of the flour mixture and mix briefly. Add half of the mashed banana and mix again. Add half of the remaining flour mixture and mix briefly, then add the rest of the mashed banana, and the remaining flour mixture. Use a rubber spatula to finish mixing. Do not overmix with the mixer!
Spread the batter in an even layer and bake for 20 to 30 minutes, until a toothpick inserted 1 inch from the edge of the pan comes out clean. Place the cake on a wire rack to cool to slightly warm or room temperature.
Make the Frosting: Using an electric mixer, beat the powdered sugar, butter, cream cheese, heavy cream, cocoa powder, and salt on low speed until combined, then increase the speed to medium high and beat until light and fluffy, 1 to 2 minutes, stopping to scrape the bowl once or twice.
Spread the frosting over the cake and serve. The cake can be stored, covered with plastic wrap, at room temperature for up to 3 days.