Prepare the Cabbage: Place the finely minced cabbage in a bowl, sprinkle with a pinch of salt, and let sit for 10 minutes. Squeeze the cabbage firmly in your hands to drain away all excess water (this prevents soggy dumplings).

Mix the Filling: In a large bowl, combine the ground pork, squeezed cabbage, grated garlic, ginger, soy sauce, sesame oil, and sugar. Knead vigorously with your hands until the meat is pale and sticky.

Wrap the Gyoza: Place a spoonful of filling in the center of a wrapper. Wet the edge with water. Fold the wrapper in half, pinching and pleating the front edge while keeping the back edge flat to seal it tightly into a crescent shape.

Fry the Bottoms: Heat the vegetable oil in a large non-stick skillet over medium-high heat. Arrange the gyoza flat-side down. Cook for 2 to 3 minutes until the bottoms are deeply golden brown and crusty.

Steam and Crisp: Pour the 1/4 cup of water directly into the hot skillet and immediately cover with a tight lid. Let them steam for 3 to 4 minutes until the water evaporates and the wrappers are translucent. Remove the lid to let the bottoms crisp back up for 30 seconds. Serve with a soy-vinegar dipping sauce.