Mix the ground pork, cabbage, mushrooms, green onions, garlic, ginger, egg, and cornstarch together in a large bowl. Let sit for 10 minutes.
In a separate bowl, mix chicken stock and water. Set aside.
Open the gyoza wrappers and place the first one on a plate. Cover the remaining wrappers with a damp cloth until ready to use.
Place 1 tablespoon of the filling in the middle of the wrapper. Wet the edges of the wrapper with water, and fold one side over to the other and seal. Repeat with remaining gyoza wrappers.
Heat a skillet or wok over medium heat and brush with oil. Place 6-8 dumplings in the pan and do not touch for 2 minutes.
After 2 minutes, pour 1/3 cup of the stock-water mixture into the pan and immediately cover. Let steam for 2 additional minutes without touching.
Carefully remove the lid and gently remove the dumplings. If they continue to stick, add another small amount of water to help them loosen up. Deglaze and/or wipe the pan between batches and repeat until all dumplings are cooked. Serve immediately.