Step 1 – Place mince, cabbage, green onion, sesame oil, soy sauce, ginger and garlic in a bowl. Mix to combine. Place 1 wrapper on a flat surface. Spoon 2 level teaspoons of mince mixture on 1 half of wrapper. Brush edges with cold water. Fold wrapper over to enclose filling. Press edges together to seal. Repeat with remaining mince mixture and wrappers.
Step 2 – Heat half the vegetable oil in a large frying pan over medium-high heat. 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 or until cooked through and wrappers have softened. Repeat with remaining oil and dumplings.
Step 3 – Meanwhile, make Dipping sauce: Combine soy sauce and vinegar in a small bowl. Serve gyoza immediately with dipping sauce.