Preheat the oven to 350°F and spray a 9x13-inch baking dish with cooking spray.
In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, and salt.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and sugars on medium speed for 3 to 4 minutes, until light and fluffy.
Add the eggs one at a time, mixing well after each addition until incorporated. Scrape down the sides of the bowl, then add the milk, bananas, and vanilla extract. Mix on medium speed for 1 minute until combined.
Add the flour mixture in 2 additions, mixing on low speed just until combined after each addition. Be careful not to overmix.
Pour the batter into the prepared baking dish and spread into an even layer. Bake for 35 minutes, until the center is set and a cake tester inserted in the middle comes out clean. Cool completely in the pan.
To make the frosting, place the cream cheese and butter in a large bowl. Beat on medium-high speed for 2 to 3 minutes, until smooth and fluffy. Add the powdered sugar and vanilla extract and beat until smooth and fluffy.
Once the cake is completely cooled, spread the frosting evenly on top. Cool it in the fridge for 20 minutes to make cleaner cuts and cut into 24 squares.