Prep shiitake: Soak shiitake mushrooms in a bowl of water for a couple hours until hydrated. Or if you're short on time, soak them in hot water for 20-30 minutes until soft. Squeeze out excess liquid from the hydrated shiitake - save this liquid plus the soaking liquid for cooking the gyoza. Finely chop shiitake.Tip: Shiitake can be quite dirty, so strain the soaking liquid through a fine sieve before using it to cook the gyoza.
For frozen tofu: Make sure your tofu is completely thawed. To do this, you can take the tofu out of the freezer a night or two before and thaw in the fridge. Or, if you don't have that much time, boil in water for 10 minutes or so until thawed all the way through.
Press tofu: Remove excess water from tofu using a tofu press or nut milk bag. Or crumble the tofu and squeeze water out by hand.
Parcook veggies: Add cabbage (and shiitake mushrooms if using fresh) to a microwave-safe bowl with a tablespoon of water, cover, and microwave 1-2 minutes, until cabbage is slightly tender but still crisp (mushrooms should be slightly soft and start to release some liquid).
Remove excess liquid: Let the veggies sit until cool enough to handle, then use your hands, cheesecloth, or a nut milk bag to squeeze out excess liquid.
Mix: Crumble tofu into a big mixing bowl and add in the cooked veggies, chives, garlic, ginger, miso, soy sauce, sesame oil, salt, and pepper. Mix until well combined.
Wrap the Gyoza
Gather your filling, gyoza wrappers, and a small bowl of water at your work space. Line a large baking sheet with parchment paper or lightly dust with cornstarch to prevent the gyoza from sticking.
Place a gyoza wrapper in the palm of your hand. Dip one finger in water and wet the edges of the gyoza wrapper.
Place about 1 tbsp of filling in the center of the wrapper. Fold the wrapper in half over the filling.
Pinch the wrapper together and use your thumb and index finger to make pleats in the top half of the wrapper. Press the pleats into the back half of the wrapper to seal the gyoza. You can make pleats going in one direction the entire way, or going towards the center in both directions.
Place wrapped gyoza in a single layer on your prepared baking sheet. Repeat the process with the remaining filling.
Cook the Gyoza
Heat a pan over medium heat and add a thin layer of oil (about 1 tbsp). Add gyoza to the pan, flat side-down, making sure they don’t touch each other. Fry the bottom of the gyoza for 1-2 minutes until crispy and browned on the bottom.
Add about ¼ cup water (or strained shiitake liquid) to the pan and cover with a lid. Reduce heat to medium low and steam for 3-5 minutes until most of the water evaporates and gyoza skins look translucent.
Remove lid and evaporate the remaining water. Cook for another minute or so until crisp on the bottom. Remove from pan and repeat the process with remaining gyoza.
Serve
Mix together dipping sauce ingredients and distribute into individual sauce bowls.
Serve gyoza immediately while hot.
Notes
1) Tofu: Frozen tofu will produce a chewier texture while fresh tofu will be more soft. If using fresh tofu, be sure to press it to get most of the water out. I like to put my tofu in a nut milk bag* and squeeze out the water.2) Dried Shiitake: Dried shiitake has a more concentrated flavor, but you can also use fresh shiitake.3) Chives: If you can't find chives, you can also use 3-4 green onions.4) Gyoza Wrappers: Some gyoza wrappers contain egg, so make sure you check the packaging if you want this dish to be completely vegan. If you can't find egg-free gyoza wrappers, try wonton wrappers as these usually do not contain egg.