Preheat your oven to 350°F (175°C). Grease your donut pan lightly with cooking spray or butter.
In a large mixing bowl, whisk together the flour, brown sugar, salt, cinnamon, nutmeg, and baking powder.
In a separate bowl, mash the ripe bananas until smooth. Add the melted butter, egg, and vanilla extract. Mix until smooth.
Pour the banana mixture into the bowl of dry ingredients. Gently fold together with a spatula until just combined.
Spoon the batter into the prepared donut pan, filling each cavity about 3/4 full.
Bake for 10-12 minutes, or until a toothpick comes out clean.
Let the donuts cool in the pan for 5 minutes, then transfer to a cooling rack.
Beat the cream cheese and butter together until smooth. Gradually add the confectioners' sugar and milk to reach desired consistency.
Frost the cooled donuts with the cream cheese frosting.
Sprinkle chopped walnuts on top of the frosted donuts.
