01 - Preheat oven to 350°F and lightly grease a 12-cavity donut pan with cooking spray or butter.
02 - Mash bananas in a large bowl until smooth. Whisk in melted butter and brown sugar until fully incorporated.
03 - Beat in eggs one at a time, then stir in milk and vanilla extract until mixture is uniform.
04 - In a separate medium bowl, sift together flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
05 - Gently fold dry ingredients into wet mixture just until combined. Stop mixing as soon as flour disappears to prevent tough donuts.
06 - Transfer batter to a piping bag or use a spoon to distribute evenly among donut pan cavities, filling each about three-quarters full.
07 - Bake for 10-12 minutes until donuts are set and a toothpick inserted into the center comes out clean.
08 - Let donuts rest in pan for 5 minutes before carefully removing to a wire rack. Cool completely before glazing.
09 - Whisk powdered sugar with 1 tablespoon milk and vanilla until smooth. Add remaining milk if needed for drizzling consistency. Dip cooled donuts tops or drizzle glaze over them.