Preheat the oven to 350°F (175°C). Grease and flour a 9×9 inch square baking pan.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, cream the softened unsalted butter and granulated sugar together until light and fluffy, about 3-4 minutes.
Beat in the eggs one at a time, mixing well after each addition.
Add the vanilla extract and mashed ripe bananas to the butter mixture and mix until combined.
Alternately add the flour mixture and the sour cream and whole milk to the banana mixture, beginning and ending with the flour mixture. Mix just until combined; do not overmix.
Pour the batter into the prepared baking pan and spread evenly.
Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan on a wire rack for 15 minutes.
After cooling, remove the cake from the pan and let it cool completely on the wire rack before serving.