Preheat oven to 350. Spray a 9x13 inch pan heavily with cooking spray.
In a small sauce pan melt 3 tablespoons butter over medium heat, stirring throughout until butter begins to brown (but not burned!). Aroma will be strong. Remove from heat. Transfer browned butter to a large bowl. Add brown sugar, honey, mashed bananas, and vanilla. Mix well. Stir in buttermilk, eggs, and oil. In another bowl combine flour, salt, and baking soda and whisk to combine. Add dry ingredients to wet ingredients and mix until incorporated. Pour into prepared pan and bake 35-45 minutes or until an inserted toothpick comes out clean. Remove from oven and allow to cool completely.
Prepare the frosting. Cream together sugars and butter. Stir in milk and vanilla. (Add just enough milk so that the frosting comes together and is spreadable) Spread frosting on cooled cake. Allow frosting to set before slicing and serving. Store in airtight container at room temperature.