01 - Preheat the oven to 350°F. Lightly grease a standard 12-cavity donut pan with butter or nonstick spray.
02 - In a large mixing bowl, whisk together the mashed bananas, melted butter, brown sugar, milk, eggs, and vanilla extract until smooth and well blended.
03 - In a separate bowl, whisk together the all-purpose flour, baking powder, baking soda, salt, ground cinnamon, and ground nutmeg until evenly distributed.
04 - Gently fold the dry ingredient mixture into the wet ingredients until just combined. Be careful not to overmix, as this can make the donuts dense.
05 - Spoon the batter into the donut pan cavities or use a piping bag for more precision, filling each one about two-thirds full.
06 - Bake for 12 to 15 minutes, or until a toothpick inserted into the center of a donut comes out clean.
07 - Let the donuts rest in the pan for 5 minutes, then transfer them to a wire cooling rack to cool completely.
08 - If using the glaze, whisk together the powdered sugar, milk, and a pinch of cinnamon until smooth. Drizzle over the cooled donuts and allow to set before serving.