Mash bananas in a large bowl until almost smooth. Use an electric mixer or fork to do this. Add the granulated and brown sugars. Mix until combined. Add the melted butter and eggs and mix until smooth. Mixture will be thin. Stop the mixer and add the dry ingredients. Mix until a batter forms. Add the milk and vanilla extract. Mix until just combined
Spread batter into the prepared pan.
Bake until golden brown, about 30 minutes.
Store cake wrapped on the counter for up to three days. Freeze cooled and frosted cake for up to three months.
Beat together cream cheese and butter until light and fluffy. Add powdered sugar and vanilla extract. Mix until smooth. Spread on cooled cake.