In a bowl, toss the cabbage with 1/2 teaspoon salt. Set aside for 15 minutes to draw excess moisture from the cabbage. Drain in a strainer and rinse with water. Squeeze the cabbage in your hands to remove more moisture.
Transfer the cabbage to a bowl and add the garlic, ginger, Chinese chives, pork, and shrimp. Stir the ingredients so they come together. Add salt, sugar, pepper, soy sauce, sake, and sesame oil and combine well.
Scoop up about 1 tablespoon of filling and put it in the center of a gyoza wrapper. Fold, pleat, and press to enclose the filling into a pleated crescent shape. Place the finished dumplings on a plate lined with parchment paper (to avoid the bottom sticking to the plate). Repeat the same until the filling is used up.
Combine some soy sauce, rice vinegar, and chili oil in a small bowl to create dipping sauce. Taste and adjust the flavor according to your liking.
Heat up a non-stick skillet over medium-high heat and add 1 1/2 tablespoons canola oil. Add the dumpling one at a time, placing the sealed edges up in a winding circle pattern. Fry the dumplings for 1-2 minutes, until they are golden or light brown at the bottom.
Add 1/4 inch (0.6cm) depth of water into the skillet and cover it immediately with its lid and lower the heat to medium. Let the water bubble away until it's dry, for about 6-8 minutes. After the water is gone, remove the lid and fry for another 1-2 minutes until the bottoms are brown and crisp. Transfer the dumplings to a serving plate and serve immediately with the dipping sauce.