• Use non-stick cooking spray to grease a 9 by 13-inch pan and preheat the oven to 375 degrees F.
• In a large bowl, combine the butter and sugar. Add the bananas, sour cream, eggs, and vanilla extract.  
• Just until moistened, add the flour, baking soda, and salt. If walnuts are being used, stir them in.
• In the prepared pan, spread batter evenly and bake for 23-28 minutes, or until a toothpick inserted in the center comes out clean. As the bars bake, make the frosting.

For the Brown Butter Frosting:

• Melt the butter over medium heat in a large skillet. When it begins to turn a delicate brown and has a nutty aroma (watch carefully so you don't burn the butter!) remove it from the heat.
• Add the powdered sugar, vanilla extract, and milk and whisk until smooth. It may be necessary to add a little more powdered sugar, or milk if the frosting needs to be thickened or thinned. 
• Over the warm bars, pour the warm frosting.  Use a spoon to spread gently.