Preheat oven to 350°F.
Whisk flours, baking soda, salt, nutmeg and cinnamon together in a large mixing bowl. Set aside.
Melt butter. Set aside.
In a separate mixing bowl, mash bananas with a fork. Mix in butter, both sugars, milk, egg and vanilla. Stir until well combined.
Combine wet ingredients into dry ingredients. Stir until just combined - do not over mix.
Fold in half the walnuts.
Spoon batter evenly into 12 greased or paper lined muffin cups.
Sprinkle remainder of walnuts over top of muffins.
Bake for about 22 - 26 minutes or until muffins are golden brown and toothpick inserted into center comes out clean.
Let muffins rest in pan on wire rack for 5 minutes. Remove from pan and let cool completely on rack.