Preheat oven to 350°F and line a muffin pan with four liners (or grease).
In a medium bowl, completely mash banana with a potato masher or fork. Add sugar, egg white, and oil. Stir with a spoon until just combined (mixture will still be lumpy).
Add flour, baking powder, baking soda, salt, cinnamon, and nutmeg. Stir until just combined. If desired, stir in optional chocolate chips.
Divide mixture between the four prepared muffin cups, filling each about 2/3 of the way full. Bake for 18 to 25 minutes, until a toothpick inserted into the center of the muffins comes out mostly clean and the tops of the muffins begin to turn golden.
Cool in the pan until cool enough to handle before transferring to a cooling rack to cool completely.