Sift the flour and baking and powder into a bowl. Add the sugar. Mix together the mashed banana, milk, butter, egg and vanilla extract. Pour into the dry ingredients and mix until well combined. Pour into a greased 9 inch pie dish and place on a baking sheet.
To make the topping, place the brown sugar, corn syrup and water in a small pot and bring to a boil. Drizzle the mixture carefully over the pudding, then bake for 30-40 minutes or until it feels slightly firm in the center.