Combine shredded napa cabbage and salt in a medium bowl. Let stand for 15 minutes to draw out the water, then transfer to a thin, clean kitchen towel and wring out as much moisture as possible. Rinse and dry the bowl the cabbage was salted in and return the cabbage to the bowl.
Add ground pork, minced garlic, minced ginger, green onions, soy sauce, toasted sesame oil, sugar, salt and pepper to cabbage and mix until combined.
Place gyoza or dumpling wrappers on a flat surface and place a rounded teaspoon of filling in the center of each. Brust the edges of the wrappers with water and fold in half to make a half-moon shape, pressing out the air and sealing the edges. If desired, lightly pleat the edges.
Place the sealed dumplings seam side up on a baking sheet lightly dusted with cornstarch, gently pressing the dumplings down to flatten their bottoms. Allow to rest for 30 minutes.
Make the dipping sauce. Bring all ingredients to a boil in a small sauce pan. Let cool slightly and transfer to a small bowl.
Heat large, preferably nonstick, skillet over medium-high heat. When hot, add 2 tablespoons of vegetable oil. Add 20 to 25 dumplings to the skillet in a circular pattern so their sides touch. Let cook until golden brown on the bottom, about 2 minutes.
Add 2/3 water to the skillet, cover, and cook until the water has almost completely evaporated about 6 to 8 minutes. Carefully uncover and cook the dumplings until crisp 1 to 2 minutes longer. Remove from heat and let sit for 2 minutes. Somethings the dumplings will fuse together. If they have you can invert the whole mess of dumplings onto a serving plate so the browned bottom side is facing up. Serve with the dipping sauce.