Preheat oven to 180° C. Grease and line a nine-inch by four-inch loaf tin.
Sieve whole wheat flour, refined flour, baking powder, salt, cinnamon powder and nutmeg powder. Cream butter and brown sugar together in a bowl till light. Add mashed bananas, vanilla essence and mix.
Beat eggs with a hand blender till light and fluffy. Add one third of the flour mixture to the banana mixture. Add one third of the beaten eggs and mix with a light hand. Again add one third of the flour and one third of the eggs and mix.
Add the remaining flour, walnuts and the remaining eggs and mix. Add milk to correct the consistency of the batter.
Transfer the batter into the prepared tin and place it in the preheated oven.
Bake at 180°C for about thirty minutes. Check if it is done by inserting a skewer. If it comes out clean it is done. If not, keep the tin back in the oven and bake for another five to ten minutes. Turn over onto a rack and cool before slicing.
You can serve this cake hot or cold.