Heat oven to 350°F. Grease and flour two 8" or 9" cake pans.
Heat a sauté pan over medium-high heat. Add 1/4 cup butter, 2 tablespoons of brown sugar and 2 cups sliced bananas to the pan. Cook until the bananas are sweet and caramelized, about 5-7 minutes. Mash caramelized bananas with a fork and set aside.
Whisk the flour, baking powder, baking soda, and salt together. Set aside.
Using a handheld or stand mixer fitted with a paddle attachment, beat the butter on high speed until smooth and creamy, about 1 minute. Add white sugar and remaining 1/2 cup of brown sugar and beat on high for 2 minutes until creamed together.
Add the eggs and the vanilla. Beat until combined. Beat in the caramelized bananas.
With the mixer on low speed, add the buttermilk and dry ingredients alternating in three additions. First the flour mixture, then buttermilk, then flour mixture etc. Do not over mix.
stir in 3/4 cup walnuts.
Pour the batter into the prepared pans. Bake for 40-45 minutes. Baking times may vary. The cakes are done when a toothpick inserted in the center comes out clean.
Remove the cakes from the oven and set on a wire rack. Allow to cool completely.
Carefully slice the tops off both cakes, to even them out for stacking and frosting. You can make a two layer cake, or slice each layer in half to make a 4 layer cake.
While the cakes are cooling, make the frosting. In a large bowl using a handheld or stand mixer fitted with a whisk attachment, beat the chilled heavy cream, vanilla and 1/4 cup sugar together on high speed until stiff peaks form.
spread each cake layer with whip cream frosting and remaining banana slices. Cover the outside of cake with frosting and decorate with remaining walnuts and white chocolate.