Place the chopped cabbage in a bowl, sprinkle lightly with salt, and let it sit for 10 minutes. Squeeze out excess moisture thoroughly.
Add garlic, ginger, green onions, soy sauce, and sesame oil to the cabbage. Mix until well combined.
Place one dumpling wrapper on a flat surface. Add about 1 tablespoon of filling to the center.
Moisten the edges of the wrapper with water, fold, and seal tightly. Repeat with remaining wrappers.
Heat neutral oil in a large nonstick or cast-iron skillet over medium-high heat.
Arrange dumplings flat-side down in a single layer and cook for 2–3 minutes until the bottoms are golden brown.
Carefully add ¼ cup water to the pan and immediately cover with a lid.
Steam for 4–5 minutes until the filling is cooked through.
Remove the lid and cook for another 1–2 minutes until the remaining water evaporates and the bottoms re-crisp.
While the dumplings cook, whisk together all dipping sauce ingredients in a small bowl.
Serve dumplings hot with soy dipping sauce on the side.