In a bowl, combine the flour and salt. Mix with a wooden spoon or chopsticks. Add hot water and stir for 2 minutes until you have coarse crumbs.
Add cold water and continue mixing. Transfer the dough to a clean surface and knead for about 5-6 minutes until it becomes a uniform and non sticky dough. Wrap the dough in plastic wrap and refrigerate for 30 minutes.
Divide the dough into 4 equal portions. Dust each piece with cornstarch and roll it out as thinly as possible, either using a pasta machine or rolling it by hand. Dust the strips of dough again with cornstarch to prevent sticking. Cut out circles of equal size using a cookie cutter.
Filling:
In a greased skillet, sauté finely chopped onions until translucent. Add chopped Portobello mushrooms, finely shredded cabbage, and grated carrot. Cook until there is no liquid left, and the vegetables have softened.
Add ginger and salt, then mix everything together. In a bowl, combine the ground chicken, the vegetable mixture, and soy sauce. Mix well.
Assembly:
Place a half tablespoon of the chicken and vegetable mixture in the center of each dough circle. Fold the circle in half, creating a half-moon shape, and use your fingers to seal the edges to form a gyoza (you can watch a video for reference).
Cooking:
Heat a frying pan with oil over medium heat. Place the gyoza in the pan and let them fry for about 2 minutes until the bottoms become golden brown.
Add 1/4 cup of water to the pan, cover with a lid, and let them steam for about 3 minutes. Open the lid and wait for about a minute to let any remaining water evaporate.
Carefully transfer the gyoza to a serving platter. Sprinkle with chopped green onions and serve with the dipping sauce. Enjoy!