1.Grease six (125ml) muffin moulds.
2.Mix yeast with flour and milk in small bowl; cover, stand in warm place about 10 minutes or until mixture is frothy.
3.Sift extra flour and sugar into large bowl; stir in yeast mixture, egg and butter. Beat about 3 minutes with a wooden spoon until batter is smooth. Place batter in large greased bowl, cover; stand in warm place about 40 minutes or until batter has doubled in size.
4.Preheat oven to 200°C (180°C fan-forced).
5.Beat batter again. Divide batter between moulds; stand, uncovered, until batter rises three-quarters of the way up side of moulds. Place moulds on oven tray; bake about 15 minutes.
6.Meanwhile, make rum syrup; combine sugar and the water in small saucepan; stir over heat, without boiling, until sugar is dissolved. Bring to the boil; boil, uncovered, without stirring, 2 minutes. Remove from heat, stir in rum.
7.Turn babas onto wire rack set over tray; pour hot rum syrup over hot babas. Place babas on serving plates; pour syrup from tray over babas until all syrup has been absorbed.