In a small bowl, soak the dried shiitake mushrooms with warm water until they turn soft. Squeeze the water dry, discard the stems, and cut the mushrooms into very tiny pieces. If you use fresh shiitake, just discard the stems and diced finely.
Mix the Dipping Sauce ingredients in a small sauce dish and set aside.
Add the chopped cabbage, scallion, and mushrooms into the pork, stir to combine. Add all the ingredients in Seasonings and blend well.
Place a gyoza wrapper onto your palm and place 1 teaspoon of the filling in the middle of the wrapper. Lightly dab your index finger into the 1/4 cup of water and circle your finger all around the outer edge of the wrapper. Pleat and fold the wrapper (starting from one end to the other end). Make sure the gyoza is sealed tight. Repeat the same until the filling is used up.
Use a flat bottom pan to pan fry the gyoza on medium heat. Add 1 tablespoon of oil into the pan and place all gyoza in the pan and cover it with the lid. Pan-fry the gyoza for 5 minutes, or until the bottoms turn brown. Add 1/2 cup of water into the pan and turn the heat to high immediately. Cover the lid to steam and cook the gyoza for another 3-4 minutes, or until the water dries out. Turn the heat to low and pan fry the gyoza for another 1 minute to crisp up the bottom. Transfer the gyoza out onto a plate and serve immediately with the dipping sauce.
Notes
Depending on the size of your pan, you might have to pan-fry the gyoza in 2 to 3 batches.