For the fritters, sift the flour, cornflour and baking powder together into a bowl, then stir in the water and sesame oil until a smooth batter is formed.
Add the banana pieces and gently mix until completely coated in batter.
Half-fill a deep, heavy-bottomed saucepan with vegetable oil and heat until a breadcrumb sizzles and turns brown when dropped in it. (CAUTION: hot oil can be dangerous. Do not leave unattended.)
Carefully place the bananas into the oil and deep-fry until golden brown. Carefully remove with a slotted spoon and drain onto paper towels.
For the caramel, place the sugar, water and sesame seeds into a saucepan over a low heat and cook until all of the sugar has melted. Increase the heat to bring to the boil and continue cooking, without stirring, until the mixture becomes a light caramel colour.
Remove the caramel from the heat and, one at a time, dip the banana fritters into the hot caramel. Turn each fritter over with a fork to coat all over, then remove immediately and plunge into a bowl of iced water. Remove the fritter from the water and leave to drain on a wire rack while you dip the remaining fritters.
To serve, place the fritters onto plates and place a scoop of vanilla ice cream alongside.