Preheat the oven to 350°F (175°C).
Melt the butter and combine it with the brown sugar in a baking dish.
Arrange the sliced bananas on top of the butter and sugar mixture.
In a separate bowl, mix the flour, baking powder, baking soda, and salt.
In another bowl, cream the granulated sugar and melted butter together.
Add the eggs one at a time, followed by vanilla extract and milk, mixing until smooth.
Combine the wet and dry mixtures, stirring just until fully incorporated.
Pour the batter over the bananas in the baking dish.
Bake for 40-45 minutes, or until a toothpick comes out clean.
Let the cake cool for 10 minutes, then invert onto a serving plate.
