Preheat the oil to 350 degrees F in a large, deep (at least 2 quarts) pot.
Place 1 piece of the quartered banana and several small chocolate pieces at the bottom of the wonton wrapper. Sprinkle with sugar and wet the edges with water. Repeat with remaining ingredients. Wrap like a burrito and drop into the oil. Fry until golden brown and place on a plate with paper towels to soak up excess oil until ready to serve.
Sprinkle again with sugar. Place on the serving plate with a scoop of ice cream.