01 - Preheat oven to 350°F. Lightly grease a standard 12-cavity donut pan with butter or nonstick cooking spray.
02 - In a large mixing bowl, whisk together the mashed bananas, melted butter, and granulated sugar until well blended. Beat in the eggs one at a time, then stir in the milk and vanilla extract until the mixture is smooth.
03 - In a separate medium bowl, whisk together the all-purpose flour, baking powder, baking soda, kosher salt, ground cinnamon, and ground nutmeg until evenly distributed.
04 - Gently fold the dry ingredient mixture into the wet ingredients using a spatula, stirring just until combined. Take care not to overmix, as this can make the donuts dense.
05 - Transfer the batter to a piping bag or use a spoon to fill each donut pan cavity approximately three-quarters full, ensuring even distribution.
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 to cool completely before glazing.
08 - In a small bowl, whisk together the powdered sugar, milk, and vanilla extract until a smooth, pourable glaze forms. Dip each cooled donut top-down into the glaze, then return to the wire rack and let the glaze set for 10 to 15 minutes.