In a large mixing bowl, combine ground turkey, chopped green onions, shredded cabbage, minced garlic, sesame oil, soy sauce, salt, and black pepper. Mix thoroughly to blend the flavors.

Take a wonton wrapper and place a spoonful of the filling in the center. Brush the edges with water, fold the wrapper to create a half-moon shape, and pinch the edges tightly.

Heat about 1 tablespoon of oil over medium-high heat in a non-stick skillet. Fry the gyoza for approximately 3 minutes, or until the bottoms are golden brown.

Pour in 1/4 cup of water into the skillet and immediately cover it. Steam the gyoza for an additional 3-4 minutes until the water has evaporated.

Transfer the cooked gyoza to a serving platter. Serve warm with your choice of dipping sauce such as soy sauce or vinegar.