In a large bowl, mix together beef, cabbage, carrot, and onion. Stir in the egg, sugar, salt, soy sauce, and vegetable oil.
Place a large teaspoonful of filling in the center of a dumpling skin. Moisten the edges of a wonton with a few drops of water. Then fold the dumpling in half, and pinch the edges together to seal. Create a ripple pattern along the pinched edge by pinching and gently pushing together small segments of it. Repeat with remaining dumplings.
Boil the dumplings in water until they float to the top, about 5 minutes.