Preheat the oven to 375 degrees and spray a 9x13 metal pan with non-stick cooking spray.
In a large bowl using a hand mixer cream together the sugar and butter until combined. Add in the egg, sour cream, bananas, and vanilla and mix until combined.
Add in the flour, baking soda, and salt and mix until combined. Using a spatula or spoon fold in the chopped walnuts.
Spread batter into the sprayed baking pan and bake for 20-25 minutes or until a toothpick comes out clean. (Start the frosting as soon as the cake comes out of the oven)
For the frosting
Heat a saucepan on medium heat and add the butter. Simmer until butter starts to turn light brown. Remove from the heat and whisk in the powdered sugar, vanilla, and milk.
Pour frosting over warm cake and spread with a spatula and sprinkle more chopped walnuts on top.