In a large bowl whisk together the dry ingredients. In a separate bowl whisk together the sour cream and egg, gently fold them into the dry mixture. Pour brown butter into the mixture and fold together until just combined.
Spoon mixture into prepared doughnut pan, and bake for 10-12 minutes, or until the doughnuts spring back when lightly pressed. Allow doughnuts to cool a few minutes in the pan before transferring to a wire wrack to cool for a few more minutes. Once cool to the touch, dip each donut in the melted butter, then roll them in the cinnamon/sugar mixture. Return them to the wire until needed.
For the caramel:
Combine the butter, heavy cream, sugar, and salt in a heavy bottomed saucepan. Place pan over medium-high high, and, stirring constantly, bring to a boil. Be sure to break up any chunks of sugar with the whisk! Once the mixture has reached a boil, stir well once more, reduce the heat to a simmer, and cook for 8 minutes, stirring occasionally. Add bourbon, if using, and vanilla - carefully, as the mixture will bubble up as you do this - whisk together, and boil for another 2 minutes. Remove from heat and pour mixture into a heatproof glass container.
Place a donut on a small serving plate or bowl. Top with a few scoops of ice cream, some banana slices, walnuts, and caramel. Serve at once!