Preheat the oven to 375. Combine the flour, baking powder, cinnamon, and salt in a bowl. In a larger bowl, combine the mashed banana, brown sugar, milk, oil, and maple syrup. Mix until it is well combined.
Add the dry ingredients into the wet ingredients and mix until just combined, until there are no clumps remaining. Don't over mix here!
Pour the batter into a large ziplock bag (or piping bag) and cup a hole in the corner. Pipe the batter into a greased donut pan.
Bake the donuts for 8-10 minutes, until you poke the top and it doesn’t jiggle. (i used a mini donut pan, so if your donuts are regular sized, they will need a longer cook time)
While the donuts are baking, make the icing. Melt the butter in a small pan over medium heat until it browns, about 5 minutes. Pour the browned butter in a bowl and add all the remaining ingredients and whisk until the icing is smooth, with no clumps.
When the donuts are finished baking, let them cool for at least 5 minutes. Dip each donut in the icing, then put the donut on a cooling rack to let any extra icing drip off. Dive in!!