01 - Preheat the oven to 350°F. Generously grease a 9-inch round cake pan and line the bottom with parchment paper.
02 - Melt 1/2 cup unsalted butter in a medium saucepan over medium heat. Stir in the light brown sugar and cook until fully dissolved and bubbling, about 2 minutes. Remove from heat, mix in dark rum if using, and ground cinnamon.
03 - Pour the caramel mixture evenly into the prepared cake pan. Carefully arrange banana slices, cut-side down, over the caramel in a single layer.
04 - In a medium mixing bowl, whisk together all-purpose flour, baking powder, and salt until fully blended.
05 - In a large mixing bowl, cream 1/2 cup softened unsalted butter with granulated sugar using an electric mixer until mixture is light and fluffy. Add eggs one at a time, beating well after each addition. Incorporate vanilla extract.
06 - Add the dry ingredients in three batches, alternating with additions of sour cream and milk. Begin and end with the flour mixture, mixing only until just combined.
07 - Gently spread the batter over the arranged bananas and caramel. Smooth the top with a spatula to achieve an even layer.
08 - Transfer to the oven and bake for 38 to 42 minutes, or until a toothpick inserted into the center emerges clean.
09 - Allow to cool in the pan for 10 minutes. Run a knife around the edge to loosen, then carefully invert onto a serving platter. Remove parchment paper. Let cool slightly before serving.