Prepare the dough: Combine the flour and salt in the bowl of a stand mixer fitted with the paddle attachment. Add the water and knead on low speed for 8 to 10 minutes, until a stiff dough forms. (If you don’t have a stand mixer, you can combine the flour and salt in a large bowl. Make a well in the middle, pour in the water, and mix until there are no more dry spots. Knead by hand until you have a stiff dough.)
Cover the bowl with a tight lid and let rest for 10 minutes. Uncover and transfer the dough to a work surface, then knead by hand until the dough is smooth. Place the dough back into the bowl, cover, and rest for another 45 minutes while you prepare the filling.
Make the filling: Heat a large nonstick skillet with 1 tablespoon of oil over medium heat. Sauté the ginger until fragrant, about 1 minute. Add the carrot and cook for 2 minutes. Add the tofu and cook, flipping occasionally, until a brown crust forms, about 3 minutes. Add the edamame and cabbage and stir-fry until the cabbage is slightly soft, 2 to 3 minutes (you can cook longer if you prefer softer cabbage texture). Season with the soy sauce, oyster sauce, sugar, mushrooms seasoning, and salt. Toss to combine and cook until the liquid is mostly evaporated, a minute or two. Transfer the mixture to a food processor. Pulse 3 to 4 times to break down the ingredients into a coarse mixture that can hold together when squeezed. Empty into a bowl.
Assemble the dumplings: Transfer the rested dough to a work surface. Knead a few times to remove any air bubbles, then divide it into 25 equal pieces and roll each into a ball. Work with one ball at a time and cover the other balls with a towel to prevent them from drying out.
Using your palm, flatten a ball into a disc. Using a rolling pin, roll it into a circle 3½ to 4 inches in diameter. Place a spoonful of filling in the middle. Pleat into your desired shape with a tight seal (since the wrapper is fresh, you shouldn’t need any water). Repeat until you’ve used all the wrappers. (If you have any extra filling, save it in the fridge or freezer for another use.)
Cook the dumplings and make the sauce: Fill a large pot two-thirds with water and set it over high heat. Meanwhile, make the sauce by whisking together the soy sauce, black vinegar, sesame oil, and sugar in a bowl until well-combined.
Once the water comes to a boil, add a drizzle of oil and carefully add as many dumplings as you can comfortably fit in a single layer. Using a spatula, gently nudge the dumplings to prevent them from sticking to the bottom of the pot. Boil until the dumplings float to the top, then let them stay afloat for another 1 to 2 minutes, until wrinkly. Use a sieve or slotted spoon to transfer the dumplings to a bowl and repeat with the remaining dumplings.
Serve: Drizzle the sauce on top of the dumplings. Garnish with a splash of chile oil, handful of cilantro, and sprinkle of toasted sesame seeds.