In a medium bowl, combine the cabbage and salt. Toss lightly. Let sit for 10 minutes to withdraw some moisture. Place a colander over a separate bowl. Transfer the cabbage to the colander squeeze out any moisture from the cabbage. Discard the water.
In a large bowl, combine the drained napa cabbage, ground pork, shiitake, scallions, sesame oil, ginger, remaining teaspoon of salt, and white pepper. Mix well with your hands.
Put a tablespoon of filling in the middle of a dumpling wrapper. Using your finger, lightly wet half of the outer rim with water.
Fold the wrapper in half. Using your fingertips, make pleats to seal the dumpling. Repeat with the remaining wrappers and filling.
In a large non-stick pan, heat the oil over medium heat. Place 8 dumplings in the pan and fry until the bottoms turn golden brown, about 5 minutes. Add ¼ cup water (60 ml) and cover. Cook for 7-10 minutes, or until the filling is cooked through. Repeat with the remaining dumplings.