01 - Preheat oven to 350°F. Grease a 9-inch round cake pan and line bottom with parchment paper.
02 - Melt 1/2 cup unsalted butter in a medium saucepan over medium heat. Stir in 3/4 cup light brown sugar and cook until dissolved and bubbling, about 2 minutes. Remove from heat and stir in 2 tablespoons dark rum (if using) and 1/4 teaspoon ground cinnamon.
03 - Pour caramel mixture into prepared cake pan and spread evenly. Arrange sliced bananas, cut side down, over the caramel in a single layer.
04 - In a medium bowl, whisk together 1 1/2 cups all-purpose flour, 1 1/2 teaspoons baking powder, and 1/4 teaspoon salt.
05 - In a large bowl, cream 1/2 cup softened unsalted butter and 3/4 cup granulated sugar with an electric mixer until light and fluffy. Add 2 large eggs one at a time, beating well after each addition. Mix in 1 teaspoon vanilla extract.
06 - Add flour mixture to wet ingredients in three additions, alternating with 1/2 cup sour cream or Greek yogurt and 1/4 cup whole milk, beginning and ending with flour. Mix until just combined.
07 - Gently spread cake batter over the bananas and caramel, smoothing the surface. Bake for 38 to 42 minutes, until a toothpick inserted in the center comes out clean.
08 - Allow cake to cool in the pan for 10 minutes. Run a knife around the edges, then invert carefully onto a serving platter and remove parchment paper. Let cool slightly before serving.