In a large mixing bowl, combine ground pork, napa cabbage, green onions, garlic, ginger, soy sauce, sesame oil, rice vinegar, sugar, and black pepper. Mix until all ingredients are well incorporated. Cover and refrigerate for at least 30 minutes to let the flavors meld.
Place a dumpling wrapper on a clean surface.
Moisten the edges of the wrapper with a bit of water using your finger.
Add about 1 teaspoon of the pork filling to the center of the wrapper.
Fold the wrapper in half to form a half-moon shape and press the edges to seal, ensuring no air is trapped inside. For a pleated edge, make small folds along one side before sealing. Repeat with remaining wrappers and filling.
Heat 1 tablespoon of vegetable oil in a large non-stick skillet over medium heat. Work in smaller batches to ensure the dumplings cook evenly.
Arrange the dumplings in the skillet, flat side down, making sure they do not touch each other. Cook for 2-3 minutes, or until the bottoms are golden brown.
Carefully add 2-3 tablespoons of water to the skillet and immediately cover with a lid. Reduce the heat to medium-low and steam the dumplings for 5-7 minutes, or until the filling is cooked through and the wrappers become translucent.
Transfer the cooked dumplings to a serving plate. Repeat with the remaining dumplings, oil, and broth.
In a small bowl, whisk together soy sauce, rice vinegar, sesame oil, toasted sesame seeds, and green onion.
Serve the dumplings hot with the dipping sauce on the side. Enjoy!