In a large bowl, combine ground pork, chopped cabbage, green onion, garlic, and ginger.
Add soy sauce and sesame oil, and mix well. Season with salt and pepper.
Place a gyoza wrapper in your hand and add about 1 tablespoon of filling in the center.
Moisten the edges of the wrapper with water.
Fold the wrapper over the filling to create a half-moon shape.
Pinch the edges to seal the gyoza tightly.
Repeat until all filling is used, placing gyoza on a floured surface.
Heat a large skillet over medium heat and add oil.
Arrange gyoza in the skillet and fry until the bottoms are golden brown.
Add a splash of water, cover, and steam for about 5 minutes until cooked through.