Preheat your oven to 275°F (135°C). Grease and flour a 9×13-inch pan.
In a bowl, whisk together cake flour, baking powder, baking soda, and salt; set aside.
In a large bowl, cream butter and sugar until light and fluffy, about 3 minutes.
Beat in eggs one at a time, then stir in vanilla and mashed bananas until smooth.
Alternately add dry ingredients and buttermilk to the banana mixture, beginning and ending with dry ingredients. Mix just until combined.
Pour batter into the prepared pan and smooth the top with a spatula.
Bake for 60–70 minutes, or until a toothpick inserted in the center comes out clean. Allow to cool completely.
Prepare cream cheese frosting by beating together cream cheese, butter, powdered sugar, and vanilla until smooth.
Spread frosting evenly over cooled cake, slice, and serve.