Preheat the oven to 350°F (175°C) and grease a 9x13-inch cake pan.

In a large bowl, whisk together the flour, baking powder, baking soda, and salt.

In a separate bowl, cream the softened butter and sugar until light and fluffy. Add the eggs one at a time, followed by bananas, buttermilk, and vanilla.

Fold the dry ingredients into the wet ingredients until combined. Avoid over-mixing.

Pour the batter into the prepared pan and bake for approximately 45 minutes, or until a toothpick comes out clean.

Let the cake cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.

For the frosting, beat together cream cheese and butter until creamy, then gradually mix in confectioners' sugar and vanilla.

Frost the cooled cake with the cream cheese frosting and serve.