Preheat your oven to 350°F (175°C). Grease a 9-inch cake pan.
Pour the melted butter into the cake pan and sprinkle the brown sugar evenly over the butter. Arrange the banana slices on top of the sugar.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt.
In a large bowl, beat the softened butter and granulated sugar until light and fluffy. Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Gradually add the flour mixture to the butter mixture, alternating with the buttermilk, beginning and ending with the flour mixture. Mix until just combined.
Pour the batter over the bananas in the cake pan, spreading it evenly.
Bake for 40 minutes, or until a toothpick inserted into the center comes out clean. Let the cake cool in the pan for 10 minutes, then invert it onto a serving plate.