Mix together beef, cabbage, carrot, and onion in a large bowl. Stir in egg, soy sauce, oil, sugar, and salt.

Place 1 heaping teaspoon filling in the center of a wonton wrapper. Moisten wonton edges with a few drops water. Fold dumpling in half and pinch the edges together to seal. Create a ripple pattern along the sealed edge by pinching and gently pushing together small segments. Repeat to make remaining dumplings.

Bring a large pot of water to a boil. Add dumplings and cook until they float to the surface, about 5 minutes. Drain.