Whisk the flour, baking powder, salt and sugar together in a large bowl.
Mash the banana in another bowl to a smooth paste. Stir in the egg, vanilla extract and oil.
Pour the banana mixture and milk into the flour mixture and whisk to a really thick batter.
Heat enough oil for deep-frying in a deep saucepan to 150C. (CAUTION: hot oil can be dangerous. Do not leave unattended.)
Carefully drop 1 teaspoon of the batter at a time into the hot oil, using another teaspoon to tease the batter off the spoon. Add enough so the doughnut balls can comfortably fry and move around in the oil – you may need to cook these in batches. Each batch should only take 4–5 minutes to cook.
Transfer with a slotted spoon to kitchen paper to drain. Place the sugar for coating on a plate and roll the doughnut balls in the sugar. Repeat to use up all of the batter.
Enjoy the doughnuts warm.
