In a large bowl, combine the ground chicken, chopped green onions, shredded cabbage, grated carrot, minced ginger, minced garlic, soy sauce, sesame oil, cornstarch, salt, and black pepper.

Mix everything together until it's evenly combined.

Get a small bowl of water, your dumpling wrappers, and a clean plate or baking sheet ready.

Place a dumpling wrapper on your palm. Add about 1-2 teaspoons of the chicken filling to the center.

Dip your finger in water and lightly moisten the edges of the dumpling wrapper.

Fold the wrapper in half to create a half-moon shape. Pinch the edges firmly together to seal.

Continue filling and folding the dumplings until you've used up all the filling. Place the finished dumplings on the plate or baking sheet.

**Pan-Frying:** Heat a little oil in a non-stick skillet over medium heat. Place the dumplings in the skillet, flat-side down. Cook for 2-3 minutes, until the bottoms are golden brown and crispy. Add 1/3 cup of water to the skillet, cover immediately, and let the dumplings steam for about 5-8 minutes, or until the water has evaporated and the dumplings are cooked through.

**Boiling:** Bring a pot of water to a boil. Gently drop the dumplings into the boiling water. Cook for about 6-8 minutes, or until they float to the surface and are cooked through.