In a large bowl, combine ground pork, cabbage, green onions, garlic, ginger, soy sauce, and sesame oil. Mix until well combined.
Place a small spoonful of the filling in the center of a gyoza wrapper. Moisten the edges with water and fold the wrapper over the filling to create a half-moon shape, pinching the edges to seal.
Heat vegetable oil in a large skillet over medium-high heat. Place gyoza in the skillet, flat-side down, and cook until the bottoms are golden brown, about 3 minutes.
Carefully pour water into the skillet and cover with a lid. Cook until the water has evaporated, and the gyoza are cooked through, about 5 minutes.
Remove the lid and continue cooking for another 2 minutes or until the bottoms are crisp again. Serve warm with dipping sauce.