In a food processor, combine the shrimp, napa cabbage, green onions, garlic, ginger, soy sauce, sesame oil, salt, and black pepper. Pulse until the mixture is finely chopped but not pureed.
Lay out a dumpling wrapper on a clean surface. Place about 1 tablespoon of the shrimp filling in the center of the wrapper. Moisten the edges with water, fold the wrapper in half, and pinch to seal. Repeat with the remaining wrappers and filling.
Dust a large plate with cornstarch to prevent sticking and place the dumplings on it. Cover with a damp cloth to keep them moist while you prepare the rest.
To cook the dumplings, you can either steam or pan-fry them. For steaming, place the dumplings in a steamer basket lined with parchment paper and steam for about 6-8 minutes until cooked through. For pan-frying, heat 2 tablespoons of oil in a skillet over medium heat, add the dumplings, and cook for 2-3 minutes until the bottoms are golden brown. Add 1/4 cup of water to the skillet, cover, and steam for an additional 5 minutes.
For the dipping sauce, whisk together soy sauce, rice vinegar, sesame oil, ginger, and honey in a small bowl.
Serve the dumplings hot with the ginger soy dipping sauce on the side.