Place the vegetable oil into a deep, heavy-based saucepan and heat until a small cube of bread sizzles and turns golden-brown when dropped into it. (CAUTION: hot oil can be dangerous. Do not leave unattended.)
Place the sesame seeds and self-raising flour into a large bowl. Whisk in enough cold sparkling water to make a thick batter.
Dip the banana slices into the batter, then carefully lower into the hot oil. Deep fry for 4-5 minutes, or until golden-brown. Remove with a slotted spoon and drain on kitchen paper.
To serve, pile onto a serving plate and dust with icing sugar.