Whisk together flour, baking powder, baking soda, salt, cinnamon, & nutmeg and set aside.
Whisk together egg and brown sugar. Add butter, banana, vanilla, and milk, and combine well.
Add wet mixture to dry mixture, mixing with a spatula until just combined.
Add batter to a piping bag or zip top bag and pipe into donut pans. Fill ⅔ - ¾ full.
Bake 9-10 minutes, until they spring back when touched*. Cool 2 minutes in pan then turn out onto a rack.
While donuts are cooling, make glaze. Add all glaze ingredients to a small bowl. Microwave for 20 seconds and stir until smooth. Microwave for 10 seconds more if needed.
While donuts are still warm, dip the tops in the glaze, flip over, and place on a wire rack to cool completely. (Or pour warm glaze over donuts if preferred.) Glaze will harden slightly over time.
Notes
*Or cook until a toothpick inserted into the middle comes out clean.
Nutrition accounts for using 80% of the glaze.
You likely will not use all of the glaze. Store leftover glaze in the refrigerator to use in other recipes or spoon over ice cream.
Keep leftovers in an airtight container at room temperature for up to 3 days.