Transfer cabbage mixture to a mixing bowl and work together until fully incorporated. Keep refrigerated until ready to use.
To make the potstickers, lay a wonton wrapper on the work surface and put about 1 tablespoon of the filling in the center. Dip your finger in a little water and wet the edges of the wonton wrapper; this will help the potsticker seal when cooking. Bring the outside edges of the wonton wrapper together over the filling and press it together to form a pouch. Continue with the remaining wrappers and filling.
To cook the potstickers, heat the remaining oil in a very large skillet over high heat. Place all of the potstickers upright in the pan and cook, without disturbing them, until browned on the bottom, about 1 to 2 minutes. Add 1/2 cup water to the pan and immediately cover. Allow the potstickers to steam for about 3 minutes, then remove the skillet lid. Continue cooking until the water is completely evaporated.
Transfer to a platter and serve with the dipping sauce.
Yield: about 1/3 cup