Preheat the oven to 350 deg F. Grease a 9x5 loaf pan and set it aside.
In a large bowl, cream butter, 1/2 cup sugar, and brown sugar until fluffy. Add the egg and mix to incorporate. Add the vegetable oil and mix.
In a separate, small bowl, combine the dry ingredients: flour, baking soda, salt, cinnamon, and baking powder. Mix this together well. Sifting wouldn't go amiss, but isn't necessary, either.
In a third, small bowl, combine the mashed banana, milk, and cream of tartar. Important to note that the amount of milk is variable. If your bananas are green, use about 1/2 cup milk. If they're very ripe, cut the milk down to just a splash. If the milk changes, then adjust the cream of tartar as well. Overusing that will give you a very sour product :).
Second to last step is to coming all three bowls into one. The large bowl from the first step should be able to fit everything. Add the banana mixture and dry mixture slowly and alternating between the two. The point of this, I think, it just to make it easier to mix. Lastly, add the walnuts and turn them in.
Pour the batter into your loaf pan and spread til roughly flat. Sprinkle the last teaspoon of sugar onto the top and toss the pan in the oven. It should be done in about 45 minutes, but check it with a toothpick before turning off your oven.
Let the loaf cool for about 10 minutes before removing the bread from the pan. The crust softens after a few hours, making it easier to cut, but I rarely wait that long :).