01 - Preheat the oven to 350°F. Lightly grease a standard 12-cavity donut pan with butter or nonstick cooking spray.
02 - In a large mixing bowl, whisk together the mashed bananas, melted butter, granulated sugar, eggs, milk, and vanilla extract until smooth and well incorporated.
03 - In a separate medium 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, stirring until just combined. Take care not to overmix to keep the donuts tender.
05 - Transfer the batter to a piping bag or use a spoon to fill each donut cavity approximately three-quarters full.
06 - Bake for 10 to 12 minutes, or until a toothpick inserted into the center of a donut comes out clean.
07 - Allow the donuts to rest in the pan for 5 minutes, then gently transfer them to a wire rack to cool completely.
08 - In a small bowl, whisk together the powdered sugar, milk, and vanilla extract until a smooth glaze forms. Dip each cooled donut into the glaze and set aside to let the topping firm up.