Preheat oven to 350 degrees. Generously grease and flour a 9 or 10 cup bundt pan.
In a medium bowl, whisk together flour, baking powder and salt.
With an electric mixer, beat the butter and sugars until light and fluffy. Add the eggs, one at a time, beating well after each addition. Mix in vanilla.
Add the flour mixture, alternating with the buttermilk, beginning and ending with the flour. Mix in the mashed banana.
Pour the batter into the prepared pan and bake for 45-50 minutes, or until a toothpick or tester comes out clean. Move to a wire rack to cool for 10 minutes before inverting on a wire rack to cool completely.
Meanwhile, make the frosting by beating the cream cheese and butter until smooth. Gradually add the powdered sugar. Stir in vanilla. Spread or pipe frosting over cooled cake.