To make the cake: Preheat oven to 375 degrees F. Spray a 9x13 glass plan with nonstick spray.
Whisk together bananas, sugar, butter, milk, eggs and vanilla. Combine dry ingredients in a separate bowl and whisk into banana mixture. Pour into prepared pan. Bake for 30 minutes. Cake will be browned when done.
Cool while you make the frosting...
To make the frosting: Melt butter in a small saucepan over medium heat. Once butter is melted and begins to bubble a bit, it will get frothy. At this point, it will take about 3-5 minutes until butter will turn brown. You might have to stir through the froth to see the color of the butter!
Once it has a nice brown color, remove from heat and add powdered sugar 1 cup at a time, whisking until smooth each time. Once it gets too firm, add the milk and continue process until frosting is smooth.
Frost cake while still warm. Top with chopped nuts.