01 - Preheat the oven to 350°F. Grease a 9-inch round cake pan and line the base with parchment paper.
02 - Melt 1/2 cup butter in a saucepan over medium heat. Stir in brown sugar and cook for about 2 minutes, or until dissolved and bubbling. Remove from heat. Stir in rum (if using) and ground cinnamon.
03 - Pour the prepared caramel into the cake pan and spread evenly. Arrange the banana slices, cut side down, in a single layer over the caramel.
04 - In a medium bowl, whisk together flour, baking powder, and salt.
05 - In a large bowl, beat softened butter with granulated sugar until pale and fluffy. Beat in eggs one at a time, mixing thoroughly after each addition. Add vanilla extract and mix well.
06 - Add the flour mixture in three increments, alternating with sour cream and milk, beginning and ending with flour. Mix gently until just combined.
07 - Carefully spoon the batter over the bananas and caramel. Smooth the surface evenly with a spatula.
08 - Bake for 38 to 42 minutes, or until a toothpick inserted in the center emerges clean.
09 - Cool the cake in the pan for 10 minutes. Run a knife around the edges, then carefully invert onto a serving platter. Remove the parchment paper and let the cake cool slightly before serving.