Melt sugar in a small saucepot on medium heat. When sugar has melted to an amber color, add butter, stirring until melted. Remove from heat and slowly stir in cream being careful not to splatter. Pour half the caramel into a bowl and set aside. Fold bananas into remaining caramel in saucepot and return to medium-high heat. Stir to combine and cook until tender, about 2 minutes. Set aside and let cool slightly. Add ice cream, banana-caramel mixture, banana liqueur and rum to a blender and blitz until smooth. Drizzle remaining caramel down the sides of glass goblets. Pour in shake and serve.