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To make the dough: In a medium bowl, whisk together the flour and salt. Place a wet towel under the bowl to keep it from sliding, then trickle the water into the flour while stirring with chopsticks or a spatula.
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After all the water is added, continue to stir until the mixture becomes shaggy and the water is evenly incorporated.
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Once the dough is cool enough to comfortably touch, knead it by hand until it's smooth and taut, about 5 to 10 minutes. It should be fairly firm, not tacky, and shouldn't stick to your hands or the bowl. If it's sticky, add a few more tablespoons of flour as you knead.
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Place the dough in an airtight container or zip-top bag and allow it to rest at room temperature for 15 to 30 minutes, or refrigerate up to 1 day.
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To make the filling: If using Napa cabbage, rinse, pat dry, then sprinkle 1/4 teaspoon salt over the cabbage and let it sit for 10 to 15 minutes, or until it wilts and releases water. Squeeze the cabbage to drain the liquid. Salting the cabbage beforehand avoids soggy dumplings later. If using regular cabbage (or another leafy vegetable with less water content), skip this step.
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In a large skillet over medium-high heat, add 1 tablespoon oil and heat until shimmering. Add the mushrooms and garlic, season generously with the remaining salt and pepper, and cook, stirring occasionally, until the mushrooms cook down and turn golden in spots, 3 to 4 minutes. Add the mushrooms to the cabbage and wipe the skillet clean.
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Crumble the tofu until no pieces larger than peas remain. Return the skillet to medium-high heat, add the remaining tablespoon of oil, and heat until shimmering. Add the tofu and cook, stirring occasionally, until pieces begin to turn golden brown, 4 to 5 minutes.
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In a small bowl, whisk together the scallions, soy sauce, water, sesame oil, sugar, and ginger. Add the mixture to the tofu and let cook for another 2 to 3 minutes, until the tofu absorbs the sauce.
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Add the tofu to the cabbage and mushrooms and mix until well combined. Set aside while you roll out the wrappers.
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To shape: Divide the dough into six pieces. Work with one piece at a time, keeping the remaining pieces covered or in a sealed container.
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Roll one piece of dough into a short cylinder about 1" in diameter. Cut the dough into six to eight pieces (fewer for thicker skins and more for thinner ones).
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Use a small rolling pin, dowel, or pastry pin to roll each slice of dough into a circle about 3 1/2" to 4" in diameter. Try to make the edges a little thinner than the center. Flour generously and set aside, covered. Repeat with the rest of the dough.
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Place 2 to 3 teaspoons of filling in the center of a wrapper. Dampen one half of the wrapper's edge. Fold the wrapper in half and press firmly along the edge to form a half-moon shape. You can cook the dumplings as is, or press the pointed corners together, like a pair of folded hands, to make a rosebud shape.
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To steam the dumplings: Have on hand a pot with a steamer basket, or a bamboo steamer. Put 2" of water in the bottom of the pot and bring to a boil. If using a steamer, fill a large wok or skillet with enough water to come up to the rim of the steamer's bottom, but not so high that the basket touches the water, and bring to a boil.
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Line the bamboo trays or the steamer's basket with parchment to keep the dumplings from sticking. Fill with dumplings; they can be close together but shouldn't touch. Place the dumplings over the boiling water and reduce the heat to medium-low, or enough to keep the water at a gentle simmer. Cover and let the dumplings steam for about 6 minutes, or until the wrappers are no longer doughy and the filling is cooked through.
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Serve warm. Refrigerate any leftover dumplings for several days; freeze for longer storage.