Bring a large pot of lightly salted water to a boil. Add napa cabbage and cook uncovered until tender, about 1 minute. Drain in a colander, then immediately immerse in ice water for several minutes until cold to stop the cooking process. Once the napa cabbage is cold, drain well, squeezing out any excess water, and place in a large bowl. Stir in ground pork, 2 tablespoons of soy sauce, sherry, cornstarch, 1 1/2 teaspoon of minced ginger, and green onion.
Arrange half of the wonton wrappers on a large sheet of waxed paper. Brush each wrapper lightly with the egg white. Place a heaping teaspoon of the pork mixture in the center of each wrapper. Gather all 4 corners of the wonton wrapper and pinch the edges together to seal in the filling. Repeat with remaining wonton wrappers.
Bring large pot of water to a boil and drop the wontons into the boiling water. When the wontons rise to the surface, continue to cook them one minute longer. Remove with a slotted spoon as they finish cooking and place on a platter.
Dipping sauce: Mix 1/4 cup soy sauce, seasoned rice vinegar, and 2 tablespoons of shredded fresh ginger in a bowl.