01 - Preheat oven to 350°F. Lightly grease a standard donut pan with butter or nonstick 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 bowl, combine the all-purpose flour, baking powder, baking soda, salt, ground cinnamon, and ground nutmeg. Stir to distribute evenly.
04 - Gradually fold the dry ingredient mixture into the wet ingredients, stirring gently until just combined. Avoid overmixing to keep the donuts tender.
05 - Transfer the batter into a piping bag or a zip-top bag with one corner snipped off. Pipe the batter into the prepared donut pan cavities, filling each about three-quarters full.
06 - Bake for 14 to 16 minutes, or until a toothpick inserted into the center of a donut comes out clean.
07 - Allow the donuts to cool in the pan for 5 minutes, then carefully transfer them to a wire cooling 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, then return to the rack to let the icing set.