This is a favourite in my household. Gyoza wrappers are slightly thicker than wonton wrappers. The gyoza purists would advise against using wonton wrappers but I find them both interchangeable for this recipe.
Blanch shredded cabbage in hot water for 20 seconds then refresh in ice cold water. Drain and set aside.
In a mixing bowl, combine cabbage with remaining ingredients.
To fill the gyoza, have a small bowl of water ready. Place one gyoza wrapper on the palm of your hand and put a teaspoon of mixture in the middle of the wrapper. Using your finger, dab one half of the edge of the wrapper with water. Bring the edges to meet to form a semi circle and pinch the edges to seal. Repeat with the rest of the mixture.
Heat oil over medium high heat and cook gyoza in batches for 2 minutes or until brown at the bottom. Do not turn the gyoza. Add water, cover and cook until water is completely absorbed. Serve with preferred dipping sauce.