Prepare the Pan and Banana Layer: Preheat your oven to 350°F and grease an 8 x 8 x 2 inch square cake pan or a 9 x 2 inch round cake pan. Spread 2/3 cup brown sugar evenly on the bottom of the pan, then scatter the butter pieces over it. Place the pan in the oven and let the butter and sugar melt for 5-7 minutes. Once melted, stir to combine, then arrange the banana slices over the mixture.
Prepare the Cake Batter: In a separate bowl, combine the dry ingredients: all-purpose flour, whole wheat flour, baking powder, baking soda, salt, and cinnamon. Set aside. In a large mixing bowl, cream together the softened butter and granulated sugar. Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract, Greek yogurt (or sour cream), and mashed bananas until fully incorporated. Gradually add the dry ingredients to the wet mixture, stirring until just combined.
Bake the Cake: Pour the cake batter evenly over the banana layer in the prepared pan. Bake at 350°F for 30 minutes, then reduce the oven temperature to 325°F and bake for an additional 25-35 minutes. The cake is done when a toothpick inserted into the center comes out clean.
Prepare the Caramel Glaze: While the cake is baking, make the caramel glaze. In a saucepan, combine brown sugar, heavy cream, butter, and salt. Bring to a boil over medium heat, stirring constantly. Let it simmer for 2-3 minutes until slightly thickened, then remove from heat.
Glaze and Serve: Once the cake is done, pour about 2/3 of the caramel glaze over the warm cake. Let the cake cool completely in the pan before flipping it onto a plate. Reheat the remaining caramel glaze and drizzle over individual slices. Optionally, sprinkle with toasted chopped pecans and serve with vanilla ice cream or whipped cream.