01 - Preheat oven to 350°F. Grease a 9-inch round cake pan and line the bottom with parchment paper.
02 - Melt butter in a saucepan over medium heat. Add brown sugar and cook until dissolved and bubbling, about 2 minutes. Remove from heat and stir in rum, if using, and cinnamon.
03 - Pour the caramel mixture into the prepared pan, spreading evenly. Lay banana slices cut side down over the caramel in a single layer.
04 - Whisk together flour, baking powder, and salt in a medium mixing bowl.
05 - In a large bowl, beat softened butter and granulated sugar using an electric mixer until light and fluffy.
06 - Beat in eggs one at a time, mixing well after each addition. Blend in vanilla extract.
07 - Add dry ingredients to the butter mixture in three portions, alternating with sour cream and milk, beginning and ending with flour, mixing until just combined.
08 - Gently spread the batter over bananas and caramel, smoothing the surface. Bake for 38 to 42 minutes, or until a toothpick inserted in the center comes out clean.
09 - Allow cake to cool in the pan for 10 minutes. Run a knife around the edge, invert carefully onto a serving platter, and remove parchment. Let cool slightly before slicing and serving.