Melt 1 tablespoon of butter over medium heat in a seasoned 8 inch cast iron skillet. Remove from heat. Sprinkle in 3 tablespoons of brown sugar and arrange the bananas in a single layer. Set aside.
Mix the all purpose and whole wheat flours, baking soda, salt and cinnamon in a medium bowl.
Cream the sugar and butter. Whisk in the egg, yogurt and bananas until well blended. Add the vanilla extract. Combine this mixture with the dry ingredients until well blended.
Pour the cake batter over the banana, sugar and butter topping in the skillet.
Bake in the middle of the oven at 375 for 30 minutes or until a toothpick inserted in the center comes out clean.
Working quickly, invert the cake onto a wire rack or plate to cool. Serve warm.
(Don't allow the cake to cool in the skillet. You won't get to see that yummy caramelized banana topping.)