To begin, preheat your oven to 350 and spray a donut pan with non-stick spray.
To a large mixing bowl, add your butter, brown sugar and banana and whisk them together. Add your vanilla and egg and briefly mix them in.
To the same bowl, add your flour, baking powder and salt. Stir together till you have a smooth and thick donut batter.
Spoon your batter into your donut pan, to just under the top of the edge of the donut cavity. Alternatively, you can put your donut batter into a piping bag and pipe your batter into the pan (you will get a more traditional and uniform donut shape this way).
Bake in the oven for 9-11 minutes, or till the top is springy to touch. Let cool slightly before adding the cinnamon sugar topping.
To a shallow bowl, add your sugar and cinnamon and stir them together.
Lightly brush each donut with butter. Roll each donut around in the cinnamon sugar topping.
Devour!
*Stored in an airtight container these will last about a day on the counter, or up to a week in the fridge.
*The cinnamon sugar topping will not last on top of the donuts, so I recommend only applying it just before eating.