Trim 1/4 inch from the stem end of each cabbage leaf and discard. Stack 2 to 3 cabbage leaves at a time and cut crosswise into 1/4 inch wide shreds to make about 8 cups. Add salt and toss to combine. Transfer the cabbage to a colander and drain. About 1 cup of liquid will be released, especially if you squeeze the cabbage from time to time.
In a medium bowl, combine the pork, scallions, 1 tablespoon minced ginger, soy sauce, sesame oil, 2 teaspoons vegetable oil, rice wine, and sugar. Set aside.
After the dough has rested, continue kneading 5 more minutes on a lightly floured surface. The dough should be elastic, smooth and not sticky. Roll the dough into an even rope about 15 inches long. Cut the rope into 1/2 inch pieces to form about 30 pieces. Roll each piece into a ball. Flatten each ball with a rolling pin that has been lightly dusted with flour into 3 inch rounds, rolling from the center to the edges, making the center slightly thicker and the edges thinner. Cover all unused dough with a slightly damp cloth.
The chicken broth should be firm by now. Roughly chop the broth into bite sized pieces. Refrigerate until ready to use.
Squeeze any excess moisture from the cabbage. The cabbage should have the appearance of having been cooked. Add the cabbage and chopped chicken broth to the pork mixture.
Place about 2 teaspoons of pork in the center of each round of dough. Fold in half to form a half moon, and pinch one end of the half moon together.
Using your thumb and index finger, make 4 or 5 small pleats in the front piece of dough, then pinch together the other end of the dough to seal the dumpling. If necessary, brush a little water to help the dough stick together. Dust each dumpling lightly with flour.
Stand each dumpling so the rounded edge is upright.
Heat a 14 inch flat bottomed wok or skillet over medium high heat until hot but not smoking. Add 1 tablespoon oil, and carefully add 8 dumplings, rounded side up, about 1/2 inch apart. Pan fry 1 to 2 minutes, or until golden brown, gently using a metal spatula to make sure the dumplings are not sticking to the wok.
Add 1/3 cup cold water, immediately cover the wok, and cook 3 minutes. Uncover the wok, and fry 2 more minutes on medium heat, or until almost all the water has evaporated.
The dumplings should be served immediately.
Place the vinegar and the remaining shredded ginger in little condiment dishes and serve with the dumplings. Using 1 tablespoon oil for each batch, continue frying the remaining dumplings, 8 at a time.
Makes about 30 pot stickers.