Pre-heat the oven to 175ºC (350ºF). Grease whatever size cake pan you are using (mine had 16 holes for mini cakes).
Melt the butter and then whisk together with the egg, sugars, milk and vanilla. I used a food processor but you could do it by hand.
Add the remaining dry ingredients and work just until everything is combined. The batter will be thick.
Spoon or pipe into the prepared tin, to around ¾ full.
Bake for around 8-10 minutes (time may vary if you are baking larger cakes).
The doughnuts are ready when they are a little springy to the touch.
Remove from the oven and allow to cool before removing from the pan.