Preheat your oven to 350°F (175°C). Grease the 9x13 inch baking pan with butter or line it with parchment paper for easy removal.
In a mixing bowl, mash the ripe bananas until smooth. Set aside.
In a large bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy, using an electric mixer if available.
Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract and the mashed bananas.
In another bowl, whisk together the all-purpose flour, baking soda, salt, and cinnamon (if using).
Gradually add the dry ingredients to the banana mixture, stirring until just combined. Be careful not to overmix.
Pour the batter into the prepared baking pan and smooth the top with a spatula. Bake for 30-40 minutes, or until a toothpick inserted into the center comes out clean.
Once baked, remove the cake from the oven and allow it to cool in the pan for about 15 minutes before transferring it to a cooling rack to cool completely.
While the cake cools, prepare the cream cheese frosting. In a bowl, beat the softened cream cheese and butter together until smooth. Gradually add the powdered sugar and vanilla extract, mixing until fluffy.
Add milk as needed to achieve the desired spreadable consistency for the frosting.
Once the banana bread cake is completely cool, spread the cream cheese frosting evenly over the top. Slice into squares and serve.