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, and granulated sugar until smooth. Add the eggs, milk, and vanilla extract, whisking until fully incorporated.
03 - In a separate bowl, whisk together the all-purpose flour, baking powder, baking soda, salt, cinnamon, and nutmeg until evenly distributed.
04 - Add the dry ingredient mixture to the wet ingredients. Fold gently with a spatula until just combined, being careful not to overmix.
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.
07 - Allow the donuts to cool in the pan for 5 minutes, then transfer to a wire rack to cool completely.
08 - In a small bowl, whisk together the powdered sugar, milk, and vanilla extract until a smooth glaze forms. Dip each cooled donut into the glaze and place back on the wire rack to set.