Prepare the Dipping Sauce: In a small bowl, stir together the soy sauce, rice vinegar, sesame oil, sesame seeds, green onions, and red pepper flakes.
Set aside.
Cook the Vegetables: Heat 2 tablespoons (30 ml / 1 fl oz) of oil in a skillet over medium heat.
Sauté the shiitake mushrooms and spinach until the mushrooms are soft, about 5 minutes.
Remove from heat and allow to cool slightly.
Make the Filling: Place the cooked mushroom and spinach mixture, finely chopped cabbage, garlic, ginger, green onions, soy sauce, salt, and dark sesame oil into a food processor. Pulse several times until combined, then process into a thick, paste-like mixture.
Assemble the Gyoza: Working with about 6 wrappers at a time, place 1 teaspoon (5 ml / 0.2 fl oz) of the filling in the center of each.
Dip your finger in the starch slurry and moisten the outer edge of the wrapper.
Fold and Seal: Fold the wrapper in half to create a half-moon shape. You can simply press the edges to seal, or create small pleats along one side before pressing firmly to seal.
Place finished gyoza on a plate and cover with a damp towel to prevent drying while you work on the rest.
Pan-Fry the Gyoza: Heat enough of the remaining oil to coat the bottom of a large skillet with a fitted lid over medium-high heat. Carefully place 5-6 gyoza in the pan, flat-side down, and sear until the bottoms are golden brown and crisp, about 1 to 2 minutes.
Steam the Gyoza: Holding the lid to shield yourself, carefully pour ¼ cup / 65 ml (2.2 fl oz) of water into the hot skillet—it will steam and spatter. Immediately cover with the lid and reduce the heat.
Cook for 3-4 minutes, or until the water has nearly evaporated and the wrappers are tender.
Serve: Remove the gyoza from the skillet and serve immediately with the prepared dipping sauce. Wipe the skillet clean and repeat the cooking process with the remaining gyoza.
Variation: Kimchi Gyoza
For a spicy twist, omit the shiitake mushrooms, spinach, cabbage, garlic, and ginger. Instead, drain 1 lb / 500 g of kimchi and place it in a food processor with 4 tablespoons (60 ml / 2 fl oz) of tomato paste.
Add the green onions, soy sauce, salt, and dark sesame oil from the original filling recipe. Process into a paste and follow the assembly and cooking above.
Don't overfill the wrappers. About one teaspoon of filling is perfect to ensure they seal properly and don't burst while cooking.
Keep your wrappers fresh by working in small batches and covering the unused wrappers and finished gyoza with a damp cloth to prevent them from drying out.