Finely chop the cabbage and chives. This is easiest using a food processor in small batches.
Thoroughly combine the cabbage, chives, pork, shrimp, garlic, ginger, soy sauce, sesame oil, and rice wine.
Add the eggs. Sprinkle cornstarch across the mixture and stir together fully.
Set out the filling mixture, wrappers, a small bowl of water, and a baking sheet.
Lay one wrapper in your hand. Wet your index finger in the water and dampen all the way around the edge.
Place about a tablespoon of filling in the center.
Pinch the top together so you have a half-circle of dough. The back side of the circle will stay flat.
On the front, make a small pleat about a third of the way from the edge, then fold the edge over to form a second pleat. Repeat on the other side.
Place completed dumplings in a single layer on the baking sheet.
When you're ready to cook, heat a thin layer of oil in a nonstick wok or pan over medium-high heat.
Place a single layer of dumplings in the pan, not crowded. Add about half a cup of water and cover.
After 10 minutes, wrappers should be completely tender. Remove to a plate for serving!