Transfer finely chopped cabbage to a large bowl. Add salt and massage it into the leaves. Rest for 10 minutes to draw out excess liquid and then rinse cabbage with running cold water. Strain and transfer cabbage to a clean towel to squeeze out as much excess water.
Into a large mixing bowl, add cabbage and remaining filling ingredients as listed above. Mix in one direction with chopsticks or a fork until the filling becomes a sticky paste. (Optional: microwave or cook 1 tablespoon of the filling until cooked through and taste test it adjusting the seasoning as needed).
Prepare a small bowl of cold water nearby. Place dumpling wrapper on a clean working surface or in the palm of your hand. Spoon 1.5 teaspoon of the filling into the middle of the wrapper. With your index finger or a spoon, lightly dab a bit of water on the edges of the wrapper.
Fold the wrapper over to create a semi-circle. Fold and pinch the edges of the wrapper together. Place folded dumplings on a baking sheet lined with parchment paper and cover with paper towels or a damp towel to keep the dumplings moist.
Choose ONE dumpling cooking method below: To Pan Fry: Heat 1 tablespoon vegetable in a large non-stick pan on medium heat. Place dumplings bottom side down in small batches, about 12-15 pieces per batch. Fry for 1 minute and then pour 5-mm water or just enough to cover the base of the pan, cover and cook for 7-9 minutes until the water has fully evaporated. Uncover and check the bottoms if they're golden brown, if not fry for another 1-2 minutes. Remove from pan.
To Boil: Bring a large pot filled halfway with water to boil on medium-high heat. Add the dumplings in small batches. Reduce to medium heat and boil for 5-7 minutes or until they float to the top and an internal temperature of 145 F with a digital instant read thermometer. Remove the boiled dumplings with a slotted spoon and transfer straight into a large serving bowl. To prevent them from sticking to each other, drizzle a bit of oil over top and mix the dumplings together.
To Deep-Fry: Remove the fried dumplings with a slotted spoon and transfer to a wire rack or a paper towel lined plate to drain off excess oil. Heat 2 cups or 500 ml of vegetable oil in a large pan on medium heat, around 330-350 F with a digital instant read thermometer. Fry dumplings in small batches until they're golden brown on all sides, about 2-3 minutes, with an internal temperature of 145 F with a digital instant read thermometer.
