Preheat your oven to 350°F (175°C). This ensures the cobbler bakes evenly and rises properly.

In a mixing bowl, combine the sliced bananas, brown sugar, melted butter, and cinnamon. Toss gently to coat the bananas evenly. This mixture will create a sweet, caramelized filling.

If using, carefully add the dark rum to the banana mixture. You can flambé it later for added flavor, but it's optional.

Transfer the banana mixture to a greased 9-inch baking dish, spreading it evenly across the bottom.

In a separate bowl, whisk together the flour, granulated sugar, baking powder, and salt. This will be the dry mix that provides structure to the cobbler.

Add the milk, melted butter, and beaten egg to the dry ingredients. Stir until just combined; do not overmix. Overmixing can lead to a tough texture.

Pour the cobbler batter over the banana filling in the baking dish, spreading it evenly to cover the bananas.

Place the baking dish in the preheated oven and bake for 30-35 minutes, or until the top is golden brown and a toothpick inserted into the cobbler comes out clean. This ensures the batter is fully cooked.

While the cobbler is baking, prepare the caramel sauce. In a saucepan over medium heat, combine the brown sugar, heavy cream, and butter. Stir until the mixture is smooth and begins to bubble. This creates a rich, creamy sauce.

Remove the saucepan from heat and stir in the vanilla extract. Allow the sauce to cool slightly before serving.

Once the cobbler is done baking, remove it from the oven and let it cool for a few minutes. This helps the filling set slightly.

Serve warm, topped with a scoop of vanilla ice cream and drizzled with the caramel sauce. The heat of the cobbler will melt the ice cream slightly, creating a delicious contrast.