Preheat oven to 350 F. Spray the donut pan with non-stick cooking spray.
In a small bowl, mash banana.
Sift the dry ingredients (flour, baking powder, baking soda, salt, brow sugar, cinnamon, and nutmeg) into a large bowl. Make a well in the center of the flour mixture and add wet ingredients (egg, sugar, melted butter, mashed bananas, and vanilla extract), and stir to combine.
Place donut batter in a disposable piping bag and pipe batter into the donut pan. If you don't have a disposable piping bag, use a ziplock bag and simply snip one corner off. Alternatively, use a cookie scoop to control the flow of batter into the donut form. Fill the donut cavities no more than 3/4 of the way full. There will be enough batter to make 8-9 donuts.
Bake 10-15 minutes until golden brown and springs back when gently touched. Remove pan from oven and let cool for 5 minutes, before inverting onto a cooling rack. Unglazed donuts taste great dusted wiht powdered sugar, or proceed with making the glaze.
Combine all ingredients in a microwave-safe bowl. Heat in 20-second intervals until the chocolate begins to melt. Stir the melted chocolate into the remaining ingredients until a smooth glaze forms.
Once the donuts are fully cooled, dip each donut in the glaze, then let sit on wire rack until the glaze hardens. Bonus points for topping your wet glaze with chocolate jimmies.