01 - Preheat the 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, and granulated sugar until smooth. Beat in the eggs one at a time, then stir in the milk and vanilla extract.
03 - In a separate bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg until evenly distributed.
04 - Gently fold the dry ingredient mixture into the wet ingredients, stirring until just combined. Take care not to overmix 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 to the touch.
07 - Allow the donuts to 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, 1 tablespoon of milk, and vanilla extract until a smooth glaze forms. Add additional milk as needed to reach the desired consistency. Dip each cooled donut top-down into the glaze and place back on the wire rack to set.