To make the filling: Place shrimp in a food processor, and process until shrimp are finely ground; transfer into a large bowl and set aside. Working in batches, process ground beef until fine, add to ground shrimp. Add ginger, shallot, green onions, napa cabbage, soy sauce, sesame oil, salt, white pepper, and white sugar to shrimp and beef mixture; mix thoroughly until well combined.

To fill the potstickers: Place a wrapper on the work surface and add a scant teaspoon of filling in the center. With a wet finger, dampen the edges of the wrapper. Fold dough into a half-moon shape, enclosing the filling, and press and seal to remove extra air and tightly seal the edges together. It's nice to fold several small pleats in the top half of the wrapper for a traditional look before you seal in the filling. Refrigerate the filled wrappers on a parchment-lined baking sheet while you finish filling and sealing the potstickers.

Heat oil in a large nonstick skillet with a lid over medium heat. Place potstickers into hot oil, flat-side down, without crowding, and let fry until the bottoms are golden brown, 1 to 2 minutes. Turn dumplings over, and pour water over them. Cover the pan with a lid and let dumplings steam until water has nearly evaporated and dumplings have begun to fry in oil again, 5 to 7 minutes. Uncover the skillet, and let potstickers cook until all the water is evaporated and the wrapper has shrunk down tightly onto the filling, another 2 to 3 minutes.