Combine pork, ginger, garlic, green onion, soy sauce, sesame oil, egg, and cabbage in a large bowl. Stir until well mixed.

Place 1 heaping teaspoon of pork filling onto each wonton skin. Moisten edges with water and fold edges over to form a triangle shape. Roll edges slightly to seal in filling. Set dumplings aside on a lightly floured surface until ready to cook.

Arrange dumplings in a covered bamboo or metal steamer so they don't touch to prevent them from sticking together; steam until pork is cooked through, about 15 minutes.