In a large colander set over a bowl, toss the cabbage with 1 tablespoon salt and let sit for 5 to 10 minutes. Squeeze to remove the liquid.
Meanwhile, in a large bowl, combine the flour and remaining 1 1/2 teaspoons salt. Using your fingers, slowly mix in 1 cup plus 2 tablespoons cold water to form a dough. Knead until smooth, about 5 minutes. Cover with plastic wrap and let rest for at least 30 minutes.
In another large bowl, combine the pork, egg, scallions, garlic, ginger, cornstarch and sugar. Stir in 1 tablespoon soy sauce and 1 teaspoon sesame oil. Add the cabbage and stir the mixture vigorously, adding about 1/4 cup cold water, to form a paste.
Divide the dough in half and cover one half with plastic wrap. Working with the other half, roll the dough into a 3/4-inch- to 1-inch-thick log. Cut crosswise into 28 slices. On a lightly floured surface, working with 1 slice at a time and keeping the others covered with plastic wrap, shape each slice into a flat disk, then roll into a 3 1/2-inch round. Repeat with the other half of the dough to make 56 rounds.
Lightly flour a baking sheet. Holding 1 dough wrapper in your palm, place about a tablespoon of pork filling in the center. Fold the wrapper in half and press the edges together to form a half circle. Place the dumpling on the prepared baking sheet and cover with plastic wrap. Repeat with the remaining dough wrappers until all the dumplings are formed.
Bring a large pot of water to boil. Working in 3 batches, add the dumplings to the pot. Stir once to prevent them from sticking. Let the water come back to a boil, add 1 cup cold water and bring to a boil again for 1 minute. Using a slotted spoon, transfer the dumplings to a platter.
In a small bowl, combine the remaining 1/2 cup soy sauce, 1 teaspoon sesame oil, the vinegar and chili paste. Serve the dipping sauce with the dumplings.