How to Make It
In a blender, puree the strawberries with the superfine sugar. Strain the sauce and refrigerate until chilled.
Preheat the broiler. Grind the turbinado sugar in a blender; transfer to a plate. Dip the cut side of the bananas in the sugar and arrange them, sugared side up, on a baking sheet. Broil the bananas as close to the heat source as possible for 2 to 3 minutes, or until caramelized.
Place 2 caramelized banana halves in each of 6 oval bowls and add 1 scoop each of vanilla, chocolate and strawberry ice cream. Pass the sauces and the toppings at the table.