Place mince, cabbage, sesame oil, soy sauce, ginger and garlic in a bowl. Stir to combine.
Place wrappers on work surface. Make dumplings: Spoon 1 heaped teaspoon mince mixture on 1 half of wrappers. Brush edges with cold water. Fold remaining wrapper halves over to enclose filling. Press edges together to seal
Heat half the vegetable oil in a large frypan over high heat. Remove from heat. Reduce heat to medium-high. Arrange half the dumplings in pan. Cook for 1 to 2 minutes or until bases are browned. Add 1/2 cup hot water. Cover with lid. Cook for 4 to 5 minutes, adding more water if necessary. Remove from heat. Uncover. Stand for 1 to 2 minutes or until dumplings come away from pan easily. Repeat with remaining oil and dumplings.