Heat oven to 375 degrees. Grease and flour 10x15 jelly roll pan or line with parchment paper (for thicker bars use a 9x13 pan and bake for 10 minutes longer than directed). Beat first four ingredients until creamy. Blend in bananas and vanilla for one minute. Add dry ingredients and blend for one minute. Stir in nuts and spread in pan. Bake 20 to 25 minutes until golden brown. Cool slighty until warm but not hot and frost with Browned Butter Frosting (recipe below).
For the Browned Butter Frosting: Heat butter in saucepan over medium heat past the melting point until it is boiling and a delicate brown. Remove from the heat and immediately add the remaining ingredients. This should be thicker than a glaze and thinner than frosting. You can add milk to get it to the correct consistency. Using a spatula smooth over the top of the Monkey Squares immediately. The frosting will be easier to spread once it's on the warm bread.