Filling: I don't measure anything, just add about equal amounts of
Shiitake mushrooms, fresh or rehydrated
carrots
bamboo shoots, preferably the canned ones. Weird, I know, but they're crunchier.
And
About half a head of Chinese cabbage, swirled a little bit in boiling salted water. About half of the mix is cabbage when I make it.
And
A bunch of chives, as in the whole bunch
A head of garlic or however much you can stand..
A big chunk of ginger
Chop chop chop. Or food processorize, much faster. If I were to measure the little bits, about 1/8" square is about right. Or a bit smaller, but not mush.
Add
A generous dollop of sesame oil, a bit of mirin, a bit of light soy sauce. Lemon juice is good, too.
Mix mix mix. As long as you can stand, a friend of mine (Chinese! Full of ancient potsticker wisdom! Source of my wrapper recipe!) insists on 20 minutes, counter-clockwise only. I'm only good for 10, switching directions. Then let it sit around a while. In the fridge if possible. The mix needs to be drained before (and usually during) making the gyoza.
I usually end up making enough for an army, but gyoza freeze very well. The other good thing about freezing them is you can pop them straight into the wok/frying pan and they don't break up/stick to the pot as much as fresh ones do. I'm a fryer, not a boiler.
My dipping sauce: light soy sauce, lemon juice, a spoonful of chili sauce. I prefer Vietnamese garlic chili sauce, the one without any sugar, but it's hard to find outside of NA. I added marmalade once for the kids, instead of chilis, that was OK, too.
I also make dessert gyoza sometimes.. didn't have an oven the first few years in Japan. Apples, raisins and cream cheese inside, dusted with icing sugar and cinnamon outside. There are a gazillion things to do with gyoza..
Just have to figure out the wrappers! Oh, and if you're boiling, the gyoza need to be boiled twice if you're using homemade wrappers.. I have found. Still prefer fried.