01 - Preheat oven to 350°F. Lightly 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 blended.
03 - In a separate medium bowl, whisk the all-purpose flour, baking powder, baking soda, salt, ground cinnamon, and ground nutmeg until evenly distributed.
04 - Pour the dry ingredient mixture into the wet ingredients. Fold gently with a spatula until just combined. Be careful not to overmix, as this can produce a tough texture.
05 - Transfer the batter to a piping bag or use a spoon to fill each donut cavity approximately three-quarters full, ensuring even distribution.
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 invert onto a wire cooling rack. Let cool completely before glazing.
08 - In a small bowl, whisk together the powdered sugar, 1 tablespoon of milk, and vanilla extract until smooth. Add additional milk as needed to reach a dippable consistency. Dip each cooled donut top-down into the glaze, then return to the wire rack and let set for 10 to 15 minutes.