Preheat the oven to 350°F. Grease a 9 x 13-inch baking pan and set aside.
Add the softened butter and granulated sugar to the bowl of a stand mixer. Beat using a flat beater attachment on a high speed for 3 minutes, or until pale and creamy.
Add the mashed bananas, eggs, vanilla extract and salt to the creamed butter and beat on a medium speed until well combined.
Add the flour and baking powder and beat on a low speed until just combined. Add the buttermilk and beat on a low speed until smooth and combined.
Pour the batter into the prepared baking pan. Bake for 30 minutes, or until cooked through. Allow to cool completely in the pan.
To make the cream cheese frosting, add the softened cream cheese, butter, vanilla extract and salt to the bowl of a stand mixer. Beat with a wire whisk attachment on a high speed for 3 minutes, or until pale and smooth.
Add the powdered sugar, 1 cup at a time, and beat on a low speed until well combined. Increase the speed to high and beat for 2 minutes, or until pale and fluffy.
Spread the frosting evenly over the cooled cake. Slice and serve.