Preheat oven to 350°F. Spray donut pan lightly with nonstick cooking spray.
In a medium bowl, stir together sugar, egg, banana, vanilla, and melted butter until well combined. Add flour, baking powder, salt, and cinnamon, mix until just combined.
Spoon the batter evenly into the donut pan. Bake for 15 minutes or until lightly golden and firm.
Let cool for 5 minutes before removing from the pan.
While the donuts are cooling, prepare the glaze.
In a small saucepan, bring the brown sugar and milk to a boil, boil one to two minutes. Remove from heat. Stir in butter and vanilla and whisk until butter melts. Whisk in powdered sugar until smooth. Pour glaze into shallow bowl.
Immediately dip the tops of the donuts in the glaze to coat. If desired, sprinkle with nuts immediately after glazing (one at a time, the glaze hardens quickly).
Return to cooling rack. Allow at least 10 minutes for glaze to set.
Nutrition information is for one glazed donut but does not include optional nuts.
If desired, omit glaze for plain banana donuts.
Donuts are best eaten the same day that they are glazed.