Preheat the oven to 350°F (175°C). Grease the 9x13 inch baking pan.
In a mixing bowl, mash the ripe bananas until smooth. Set aside.
In another mixing bowl, beat the softened butter, granulated sugar, and brown sugar together until creamy.
Add the eggs, one at a time, mixing well after each addition. Stir in the vanilla extract.
Mix in the mashed bananas until fully combined.
In a separate bowl, whisk together the flour, baking soda, salt, and ground cinnamon.
Gradually add the dry ingredients to the banana mixture, stirring until just combined. Do not overmix.
Pour the batter into the prepared baking pan, spreading it evenly.
Bake in the preheated oven for about 40 minutes, or until a toothpick inserted in the center comes out clean.
Allow the cake to cool in the pan for about 10 minutes, then transfer it to a cooling rack to cool completely.
In a mixing bowl, beat together the softened cream cheese and butter until smooth and creamy.
Gradually add the powdered sugar and continue to mix until well combined and fluffy.
Stir in the vanilla extract. If the frosting is too thick, add 1-2 tablespoons of milk to reach desired consistency.
Once the cake is completely cooled, spread the cream cheese frosting evenly over the top.