There is the "right way" to prepare gyoza and similar dumplings. But why be limited by that. Here are several assorted gyoza variations, together with some non-traditional dipping sauces.
Cook the garlic, leeks, and carrot slowly in butter until the leeks are very soft
Cook the chopped mushrooms in batches so that they get a little browned rather than just soggy.
Allow to cool a little
Combine the vegetables, miso, egg yolk, and pepper
Fill gyoza wrappers
Asparagus, sweet potato, and ginger gyoza
Peel sweet potatoes and boil until soft. Drain and allow to cool a little.
Wash and chop the asparagus into 5mm sections
Saute the asparagus and ginger in 10g butter until fragrant. Asparagus should still be crispy.
Mash the sweet potato
Combine mashed sweet potato with asparagus and ginger.
Season with salt and freshly ground pepper.
Fill gyoza wrappers
Beef brisket and broccoli gyoza
Finely chop the heads of the broccoli. Discard the stalks (or keep for a veggie stock)
Saute the broccoli in a little olive oil for a minute or two. It should still be crisp.
Finely chop or break up the beef brisket. Combine with the broccoli, salt, and pepper.
Fill gyoza wrappers
Black garlic, black beans, and anchovy gyoza
If using uncooked black beans, cook the beans according to the packaging. I used left over beans from this recipe.
Mash the black garlics cloves and anchovies
Coarsely mash the cooked black beans
Fill gyoza wrappers
Vietnamese dipping sauce
Combine all ingredients in a bowl and stir until the sugar is dissolved
Red curry dipping sauce
Combine coconut milk and curry paste in a small saucepan over medium heat and bring to a simmer. Cook, stirring, until slightly thickened and fragrant, about 30 seconds. Remove from heat and set aside.
Meanwhile, combine lime juice, soy sauce, fish sauce, honey, and ginger in a small bowl. Add coconut-curry mixture and stir thoroughly to combine.
Soy, ginger, and chili dipping sauce
Combine all ingredients in a bowl and stir.
Cooking the gyoza
Add a little canola oil to a skillet or non-stick pan on a medium heat
Add the gyoza to the pan, maybe 5 or 6 at a time, folded edge up. Cook until the bottom has browned.
Add 1/2 cup hot water and immediately cover so that the gyoza are cooked by the steam.
After 3 or 4 minutes, remove the cover.
Drizzle some sesame oil into the pan and cook until any remaining water has boiled off and the base of the gyoza is crispy.