01 - Preheat the oven to 350°F. Grease a standard 12-cavity donut pan generously with butter or nonstick spray.
02 - In a large mixing bowl, whisk together the mashed bananas, melted butter, brown sugar, milk, eggs, and vanilla extract until smooth and well incorporated.
03 - In a separate bowl, whisk together the all-purpose flour, baking powder, baking soda, salt, ground cinnamon, and ground nutmeg until evenly distributed.
04 - Gently fold the dry ingredient mixture into the wet ingredients until just combined. Be careful not to overmix, as this can make the donuts dense.
05 - Spoon the batter into the prepared donut pan, filling each cavity about two-thirds full. Alternatively, transfer the batter to a piping bag for cleaner filling.
06 - Bake for 12 to 15 minutes, or until a toothpick inserted into the center 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 transfer them to a wire cooling rack to cool completely.
08 - If using the glaze, whisk together the powdered sugar, milk, and a pinch of cinnamon until smooth. Drizzle generously over the cooled donuts and allow the glaze to set before serving.