For the Cake:

1. Preheat the oven to 350°F. Grease two 8-inch baking pans and line with parchment paper or a silicone mat; set aside.
2. In a large mixing bowl beat butter with an electric mixer on medium speed for about 30 seconds.
3. Next add the sugar, baking powder, baking soda, and salt. Beat until all ingredients are combined, scraping sides of bowl as needed.
4. Beat in the egg, mashed bananas, sour cream, and vanilla until mix until combined.
5. Next, add the flour and walnuts, beating as much as you can using the mixer, but being careful not to overmix. Then use a wooden spoon or spatula and, stir in any remaining flour and the walnuts.
6. Pour the batter into the prepared baking pans, spreading evenly. Bake in a 350°F for 20-25 minutes. Test the cake for doneness by inserting a toothpick into the center of the cake. If the toothpick comes out clean, your cake is done. Cool completely.

For the Frosting:

1. To brown the butter, use a small saucepan, and cut the butter into pieces. Melt the butter over medium heat and allow it to boil and bubble. Once it starts boiling, stir it frequently and it will slowly start to turn an amber color and releases a nutty aroma. Remove the butter from the heat and place in the freezer for 20-25 minutes and then stir until smooth.
2. Slowly add the powdered sugar 1 cup at a time, alternating in some of the liquid ingredients (Rum, milk and vanilla). The frosting will be thick at times, but as you slowly add the liquid, it will become smoother. Beat the frosting each time you add the powdered sugar until the frosting is completely smooth, whipped and fluffy.
3. Spread 1/3 of the frosting on top of the first layer, and drizzle some caramel and chopped nuts if desired. Then spread the remaining frosting over the cooled cake. Garnish with caramel and walnuts. Store in an airtight container.