Preheat the oven to 350°F (175°C).
Melt the butter in a 9-inch round cake pan.
Sprinkle the brown sugar evenly over the melted butter.
Arrange the halved bananas over the brown sugar mixture.
In a mixing bowl, whisk together flour, baking powder, baking soda, and salt.
In a separate bowl, beat the eggs, sugar, and vanilla extract until fluffy.
Gradually mix in the dry ingredients and milk until just combined.
Pour the batter over the arranged bananas.
Bake for 30-35 minutes or until a toothpick inserted comes out clean.
Allow the cake to cool for 10 minutes before inverting onto a serving plate.
