01 - Preheat 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 - Gradually add the dry ingredient mixture to the wet ingredients. Fold gently with a spatula until just combined — do not overmix, as this can make the donuts tough.
05 - Spoon the batter into the donut pan cavities or transfer to a piping bag for cleaner filling. Fill each 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 and the tops spring back lightly when touched.
07 - Allow the donuts to rest in the pan for 5 minutes, then carefully transfer them to a wire cooling rack to cool completely before glazing.
08 - In a small bowl, whisk together the powdered sugar, milk, and vanilla extract until a smooth, pourable glaze forms. Dip each cooled donut top-down into the glaze, then return to the wire rack and let set for 10 to 15 minutes.