Place the ground pork, cabbage, garlic, green onions, salt, sugar, soy sauce, sesame oil in a mixing bowl; mix everything with your hands, knead it for two minutes or when everything is incorporated, and homogenized.
Line up as many dumpling wrappers as you can on a baking sheet, add one heaping teaspoon of meat into the center, lightly brush the perimeter with water.
To shape, close it like a taco pinching the top of the taco together, and starting with one side, crimp one part of the dough, towards the center, pinch to keep it folded, then working your way to the edge, crimp a second one over that, then the third. So now you crimped one side, then crimped the other side, make sure there are no air bubbles, and seal the seams. Repeat with all the wrappers.
In a 12-inch non-stick pan, add enough vegetable oil to cover the bottom in a thin layer and set it up on medium heat.
Add your dumplings in a circular pattern, place as many as you can without overlapping, and let them cook for two to three minutes or until the bottom turns golden brown.
Immediately add ¼ cup of water, cover with a lid, and let them steam, maintaining the temperature for three minutes.
Remove the lid and let the remaining water evaporate.