Prepare the baking pan: Preheat your oven to 350°F (175°C). Grease a 9-inch round cake pan with butter and line the bottom with parchment paper for easy removal.

Make the caramel: In a medium saucepan over medium heat, melt the 1/2 cup of butter. Once melted, add the brown sugar and stir until combined. Cook for about 2-3 minutes until the mixture is bubbly and slightly thickened. Pour the caramel mixture into the prepared cake pan, spreading it evenly across the bottom.

Arrange the bananas: Place the sliced bananas in a single layer on top of the caramel in the cake pan, arranging them in a decorative pattern if desired.

Mix the dry ingredients: In a bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.

Cream the sugars: In a large mixing bowl, beat the granulated sugar and eggs together until light and fluffy, about 2-3 minutes. Add the vanilla extract and mix until combined.

Combine wet and dry ingredients: Gradually add the dry ingredients to the egg mixture, alternating with the buttermilk. Start and end with the dry ingredients, mixing until just combined. Be careful not to overmix.

Pour the batter: Carefully pour the batter over the arranged bananas in the cake pan, smoothing the top with a spatula.

Bake the cake: Place the cake in the preheated oven and bake for 35-40 minutes, or until a toothpick inserted into the center comes out clean.

Cool and invert: Once baked, remove the cake from the oven and let it cool in the pan for about 10 minutes. Then, carefully run a knife around the edges to loosen it. Place a serving plate on top of the cake pan and quickly invert it to release the cake. Remove the pan and peel off the parchment paper.

Serve: Allow the cake to cool slightly before slicing. Serve warm or at room temperature, optionally with a scoop of vanilla ice cream or a dollop of whipped cream.