Preheat oven to 350°F. Coat the bottom and sides of a 9x13-inch cake pan with cooking spray. Cut a parchment paper sling for the short and long sides. Lightly spray the parchment paper with cooking spray.
In a medium sized bowl, combine the flour, baking powder, baking soda, and salt. Stir with a whisk and set aside.
2 cups cake flour, 2 teaspoons baking powder, ½ teaspoon salt
In a separate medium sized bowl, combine the mashed banana and buttermilk. Stir with a fork to combine.
1 ½ cups mashed ripe banana, about 4 bananas, ½ cup buttermilk
In the bowl of a stand mixer fitted with the paddle attachment, beat the sugar, butter, brown sugar, and vanilla together at medium speed for 5 minutes.
1 cup sugar, ½ cup butter, softened, ½ cup packed brown sugar, 1 tablespoon vanilla extract
Add eggs, one at a time, beating well between each addition.
3 eggs
Add the flour mixture to the sugar mixture, alternately with the buttermilk mixture, beginning and ending with the flour mixture. Mix just until combined.
Pour the batter into the prepared pan. Sharply tap pan once on the counter to remove any air bubbles.
Bake at 350°F for 25-30 minutes or until a wooden toothpick inserted in the center comes out mostly clean with a few moist crumbs and the edges are starting to pull away from the pan..
Cool in pan for 10 minutes on a wire rack. Remove from the pan and cool completely on a wire rack.