Toss the bananas in 2 tbsp of the sugar. Heat a griddle to medium, then cook the bananas, a few pieces at a time, until sticky and showing griddle marks. Keep warm in a low oven.
For the sauce, put the remaining sugar, the butter and cream into a saucepan and stir over a gentle heat until the sugar has melted. Stir in the sesame seeds. Can be made up to a day ahead. To serve, put a few pieces of banana into 8 serving dishes, spoon over some of the caramel, then top with a scoop of ice cream.