For the caramel: Place the sugar and 1/2 cup water in a medium heavy-bottomed saucepan. Shake the pan gently to distribute the sugar evenly.
Bring to a boil over medium-high heat, watching closely and swirling the pan occasionally. Remove from the heat when the sugar mixture begins to color to a dark amber color, 5 to 7 minutes.
Slowly whisk the cream and bourbon into the caramelized sugar, mixing until smooth.
Pour the sauce into a bowl and allow to cool slightly. (Sauce keeps, covered and chilled, for 2 weeks.)
Cut the bananas in half lengthwise and again widthwise. Place the pieces cut-side up on a flame-resistant surface, such as a baking sheet lined with foil. Sprinkle cut sides of each banana piece generously with the sugar and apply a flame with a brulee torch. Let the sugar caramelize until deeply golden. Place the banana pieces in a serving dish and top with the ice cream, caramel and whipped cream.
NotesCook's Note: You can also put the bananas under the broiler to caramelize if you don't have a brulee torch.