Spread 1 teaspoon of butter along the inside edge of a round 9″ metal or aluminum cake pan, avoiding the bottom. Dust with 2 tablespoons of sugar, shaking out any excess.

Heat remaining 1 cup sugar, water, and vanilla in a small heavy bottomed sauce pot over medium-high heat.

Cook sugar mixture to 350°F, brushing down the sides with water if sugar crystals appear. Caramel should be amber in color.

Remove the pot from the heat and swirl in remaining 1 tablespoon butter. Pour the caramel into the bottom of the cake pan and spread evenly.

Preheat oven to 325°F. In a mixing bowl, combine flour, baking powder, and salt.

In a stand mixer fitted with a paddle, or using a hand mixer, beat the butter and sugars together until light and fluffy, occasionally scraping sides of bowl to ensure even incorporation.

In a separate bowl, whisk together milk, vanilla, eggs, rum, and banana. Add to stand mixer and mix until combined.

Add dry ingredients and mix until batter is smooth, scraping down sides of bowl for even mixing. Add yogurt and mix until just combined.

Pour the batter over the caramel banana topping and bake for approximately 40 minutes, or until golden on top and a skewer comes out clean when inserted into the center of the cake.

Remove from oven and immediately run a knife around the edge of the cake. Let stand for 5 minutes before inverting.

Place a plate or serving platter upside down on top of cake pan. While holding them both together, very carefully flip the cake pan over on top of the plate so the cake is banana side up. Let cool slightly before slicing and serving.