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. Beat in the eggs one at a time, then stir in the milk and vanilla extract until fully incorporated.
03 - In a separate medium bowl, whisk together the all-purpose flour, baking powder, baking soda, salt, ground cinnamon, and nutmeg until evenly distributed.
04 - Pour the dry ingredient mixture into the wet ingredients. Fold gently with a spatula until just combined, being careful not to overmix. A few small lumps are acceptable.
05 - Transfer the batter to a piping bag or use a spoon to fill each donut cavity approximately 3/4 full, ensuring even distribution across all 12 cavities.
06 - Bake on the center rack for 10 to 12 minutes, or until a toothpick inserted into the thickest part 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 dip-able consistency. Dip each cooled donut top-down into the glaze, then return to the wire rack and let set for 10 to 15 minutes.