In a small saucepan, combine sugar and water. Bring to a boil without stirring and cook 10 to 12 minutes or until the mixture is a dark amber color. Remove from heat and carefully add milk. The mixture will bubble and splatter. Swirl pan and once the bubbling has stopped, whisk into a smooth caramel sauce.
Cool 10 to 15 minutes or until slightly thickened.
To serve, place ½ cup pudding in each bowl and top with sliced bananas. Sprinkle with peanutsand drizzle with caramel sauce.