Add egg to flour and mix well. Knead dough until smooth, wrap in damp cloth, and set aside for 30 minutes.
With rolling pin, roll out dough to semi-transparent thickness and cut into 3-inch squares. Sprinkle squares with cornstarch to prevent sticking and stack. (To store, wrap stacks of wrappings in foil or wax paper and refrigerate).
Mix shrimp, pork fat, dry sherry, salt, sugar and pepper. Place wrapping square with corner towards you. Dip finger in water and moisten opposite edge. Place 1/2 teaspoon filling in center of wrapping, fold corner across to opposite corner (corners should not align exactly). Pleat and press gently, but firmly, to seal.
Heat oil (360 degrees) and deep fry until golden. Serve hot or at room temperature as an hors d'oeuvre. Makes 20 wontons.
Note: Ready-made wrappings may be purchased.