Preheat oven to 350 degrees and grease a 15x10x1 inch pan.
In a large bowl cream together butter and sugar until light and fluffy. Add eggs and vanilla and mix well. Next add mashed bananas and mix well.
In a medium bowl whisk together flour, baking soda, and salt. Add to wet ingredients and mix until incorporated.
Pour mixture into prepared pan.
Bake for 25 minutes or until an inserted toothpick comes out clean. Allow to cool.
To make the frosting, melt butter in a medium sauce pan. Once melted continue to boil until butter turns from a light yellow to a dark golden yellow. (This works best in a light-colored sauce pan so you can gauge the color of the butter)
In a large bowl cream together the browned butter and cream cheese until smooth. Stir in vanilla and salt. Gradually mix in powdered sugar until completely incorporated and frosting is smooth.
Spread frosting over cooled bars. Cut and serve OR cover and store at room temperature up to three days.