In a large bowl, cream brown butter on medium speed until smooth and creamy. Add granulated and light brown sugars and mix until combined and fluffy. Add eggs one at a time, mixing well after each. Next, add the mashed banana, milk, maple extract, and cinnamon, mixing until all are completely incorporated. Then add the baking soda, baking powder, and half of the flour. Mix until just combined. Add the second half of the flour and mix well.