Step 1: Finely chop or shred the green cabbage. Place it in a large bowl, sprinkle with 1/2 teaspoon of salt, and let it sit for 10-15 minutes to draw out excess moisture.
Step 2: While the cabbage rests, finely mince the garlic and ginger. Thinly slice the green onions, separating the white and green parts.
Step 3: In a large mixing bowl, combine the ground chicken, minced garlic, minced ginger, white parts of the green onions, soy sauce, sesame oil, and a pinch of black pepper. Mix thoroughly with your hands until all ingredients are well incorporated.
Step 4: Squeeze out any excess water from the salted cabbage. Add the drained cabbage to the chicken mixture. Mix gently until just combined.
Step 5: Have a small bowl of water ready. Take one dumpling wrapper and place about 1 teaspoon of filling in the center.
Step 6: Dip your finger in water and moisten the edges of half the wrapper. Fold the wrapper in half to create a half-moon shape, pressing the edges firmly to seal.
Step 7: For a classic pleated look, start from one corner of the folded edge, make small pleats along the top edge, pressing each pleat against the unpleated bottom edge until you reach the other corner.
Step 8: Place the assembled dumplings on a parchment-lined tray, making sure they don't touch each other. Repeat with the remaining filling and wrappers.
Step 9: To steam: Arrange dumplings in a single layer in a steamer basket lined with parchment paper. Steam over boiling water for 8-10 minutes, or until wrappers are translucent and filling is cooked through.
Step 10: To pan-fry (potsticker style): Heat 1 tablespoon of oil in a non-stick pan over medium heat. Place dumplings flat-side down in a single layer. Cook for 2-3 minutes until bottoms are golden brown. Add about 1/2 cup of water to the pan, immediately cover, and steam for 5-7 minutes, or until water has evaporated and filling is cooked.
Step 11: To boil: Bring a large pot of salted water to a rolling boil. Carefully drop dumplings into the water, ensuring not to overcrowd. Cook for 5-7 minutes, or until they float to the surface and wrappers are tender.
Step 12: Serve immediately with your favorite dipping sauce, garnished with the green parts of the green onions.