Preheat the oven to 350°F (175°C) and grease a 9x13 inch baking pan.

In a large mixing bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy.

Add the mashed bananas and eggs to the mixture, and mix until well combined.

In a separate bowl, whisk together the flour, baking soda, baking powder, and salt.

Gradually add the dry ingredients to the wet mixture, mixing until just combined. Stir in the vanilla extract.

Pour the batter into the prepared baking pan and spread evenly.

Bake for 25-30 minutes or until a toothpick inserted into the center comes out clean.

Allow the bars to cool completely in the pan on a wire rack.

In a mixing bowl, beat the softened cream cheese until smooth.

Gradually add the powdered sugar and mix until well combined.

Add the vanilla extract and milk, mixing until the frosting reaches your desired consistency.

Once the banana bars are completely cooled, spread the cream cheese frosting evenly over the top.

Cut into squares and serve.