Preheat oven to 350F.

Lightly spray a 9x13 baking dish with cooking spray or line with parchment paper. Set aside.

Beat bananas and butter together in a large mixing bowl until thoroughly combined.

Add the sugars and cream together with the butter and banana mixture.

Mix in the vanilla and eggs, one at a time, mixing until completely combined.

Combine the flour, baking soda, baking powder, and salt in a small bowl and gradually add the wet mixture stirring just until combined.

Fold in optional chopped nuts.

Pour batter into prepared pan and bake for 23 to 27 minutes or until an inserted toothpick comes out clean. Let the cake cool completely.

Melt the butter in a small skillet over medium heat, stirring occasionally. The butter will start to foam and then start browning. You will be able to smell a nutty aroma when it's ready. Remove from heat and allow to cool for at least 30 minutes.

Beat browned butter and cream cheese together until completely blended, light, and fluffy.

Beat in the maple extract and powdered sugar, a half a cup at a time.

Spread frosting onto cooled cake and sprinkle on chopped nuts if desired.