Combine ground pork, squeezed cabbage, green onions, garlic, ginger, soy sauce, mirin, sesame oil, salt, and pepper in a bowl until well mixed.
Place one gyoza wrapper in your palm and add about 1 teaspoon of filling into the center.
Moisten the wrapper edge with water, fold in half, press the center, then pleat and seal the top edge to form a neat dumpling.
Arrange finished gyoza on a lightly floured tray in a single layer so they don't touch.
Heat a nonstick skillet over medium-high heat and add 1 tablespoon vegetable oil.
Place gyoza flat-side down in the hot pan, spacing them evenly and fry without moving for 2–3 minutes until the bottoms are golden brown.
Carefully pour about 1/4 cup water into the pan per batch (roughly 12–14 gyoza) and immediately cover with a tight-fitting lid to steam.
Steam the gyoza for 4–5 minutes, until the water has mostly evaporated and the wrappers are tender and cooked through.
Remove the lid and continue cooking 30–60 seconds to re-crisp the bottoms, then transfer gyoza to a plate.
Repeat with remaining gyoza. Serve hot with the prepared dipping sauce.