In any case, this is my version of a pork gyoza which is probably very similar to what my mother made and it is also similar to the ones we had in a Izakanya in Japan last time. The skin or casing available in a regular grocery store in the U.S. is called "Wonton" skin and is rather thin and square as opposed to a Japanese version which is round (you could buy them at a Japanese grocery store frozen). I do not see much difference except for the cosmetic appearance and am happy with the American version of "wontan" skins for my gyoza.
For a filling, I use pork (usually the trimmings of the pork tenderloin which I hand chop). I mix the pork with finely chopped precooked cabbage leaves, grated ginger root, finely chopped garlic and scallion with a dash of dark sesame oil, soy sauce, mirin, cracked black pepper and salt. I also sometimes add finely chopped shiitake mushroom. (Unfortunately I usually "eyeball" all the ingredients but the proportion of vegetable and meat can be varied). I try not to over season since it is eaten with an additional dipping sauce and Japanese hot mustard. Knead or mix the meat mixture well.
To form the gyoza, take one sheet of the wanton skin in your left palm (I am right handed) and wet two neighboring edges with water using your finger tip. Put scant 1 tsp of the filling in the center and fold to make a triangle so that the two wet edges are pressed against the two dry edges. Try to squeeze out any trapped air around the filling and press the edges to seal. Using your right thumb and index finger pinch and make several crimps along the sealed edges. You should assemble the gyoza just before cooking otherwise the skin will get wet and sticky.
Place the gyoza in a large enough non-stick frying pan (large enough so that gyoza can be placed in one layer comfortably) on medium high heat. Add 1tbs of peanut oil and a splash of dark sesame oil. When oil is hot add gyoza in one layer without touching each other one at a time. When one side is browned (1-2 minutes) turn them over to brown the other side (This is not the traditional way of doing this. Traditionally, the gyoza are placed together to make a neatly arranged circle to fill the pan and only one side is browned. After cooking is completed, they are inverted on a serving plate en mass but I like to brown both sides). Then add 1/3 cup of hot water into the pan (be careful, it will boil and steam immediately) and put a tight lid on. Steam will come out from the edge of the lid or steam hole if your lid has one. (I sometimes have to put the measuring cup on the lid to hold the lid down against the force of the steam). Cook for about 5 minutes or until the amount of steam decreases. Open the lid and the water should be almost all gone. Make sure all the water is gone and the bottom becomes brown and crispy again. For dipping sauce, I make a traditional mixture of rice vinegar and soy sauce (half and half) with Japanese hot mustard.
I served this with a celery salad. We had this celery salad for the first time in Kurashiki 倉敷 in south western mainland Japan, when we went to a smoke-filled small hole-in-the-wall drinking place just across from the train station. Thinly sliced celery was simply dressed with powered kelp tea or "kobucha" 昆布茶 instead of using salt．I also add a very small amount of olive oil.