01 - Preheat oven to 350°F. 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, whisk together 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. Stir gently with a spatula until just combined. Avoid overmixing to keep the donuts tender.
05 - Spoon or pipe the batter into the prepared donut pan, filling each cavity about 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 - Let the donuts rest in the pan for 5 minutes, then transfer them to a wire rack to cool completely.
08 - In a small bowl, whisk together the powdered sugar, milk, and vanilla extract until smooth. Dip each cooled donut into the glaze, then place back on the wire rack to set.