01 - Preheat the oven to 350°F. Grease a 9-inch round cake pan and line the base with parchment paper.
02 - In a medium saucepan over medium heat, melt 1/2 cup butter. Stir in brown sugar and cook until fully combined and bubbling, about 2 minutes. Remove from heat and mix in dark rum (if using) and ground cinnamon.
03 - Pour the caramel mixture into the prepared pan, spreading it evenly over the bottom. Arrange the sliced bananas, cut side down, in a single layer over the caramel.
04 - In a medium bowl, whisk together flour, baking powder, and salt. In a separate large bowl, cream 1/2 cup softened butter with granulated sugar using an electric mixer or whisk until light and fluffy. Add the eggs one at a time, beating well after each addition. Blend in the vanilla extract.
05 - Add the flour mixture to the creamed mixture in three parts, alternating with sour cream and whole milk, beginning and ending with the dry ingredients. Mix until just combined.
06 - Gently spread the batter over the arranged bananas and caramel. Smooth the top with a spatula.
07 - Bake for 38 to 42 minutes, or until a toothpick inserted in the center comes out clean.
08 - Allow the cake to cool in the pan for 10 minutes. Run a knife around the edges, then carefully invert onto a serving platter. Remove the parchment and let the cake cool slightly before serving.