01 - Preheat the oven to 350°F. 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, granulated sugar, eggs, milk, and vanilla extract until smooth and well incorporated.
03 - In a separate bowl, whisk the all-purpose flour, baking powder, baking soda, salt, ground cinnamon, and ground nutmeg until evenly distributed.
04 - Add the dry ingredient mixture to the wet ingredients and fold gently with a spatula until just combined. Avoid overmixing 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 and the tops spring back lightly when touched.
07 - Allow the donuts to rest in the pan for 5 minutes, then transfer them to a wire rack to cool completely before glazing.
08 - Whisk the powdered sugar, milk, and vanilla extract together until smooth. Dip each cooled donut halfway into the glaze, then return to the wire rack and let the glaze set.