Make the all-purpose soy dipping sauce:

In a nonreactive bowl, mix all the sauce ingredients together and leave at room temperature to use, or make ahead and refrigerate for up to 3 weeks.

Make the mandu:

In a bowl, break the noodles and cover with warm water for 15 to 20 minutes to rehydrate. Drain, then chop the noodles into pieces no longer than ½ inch. You need ½ cup chopped noodles for the filling.

In a large skillet, heat 1 tablespoon oil over medium heat. Add the onion and cook, stirring often, until deep golden brown, about 10 minutes, lowering the heat or adding a splash of water to the pan if the onions begin to brown too much. Let cool to room temperature, then transfer to a large mixing bowl.

In the same bowl, add the noodles, beef, garlic chives, garlic, sesame oil, soy sauce, mirin, sugar, pepper and salt. Using your hands, mix the filling together until well mixed. Cover and refrigerate at least 30 minutes to ensure the filling is cold before shaping the dumplings.

Before filling the dumplings, line a sheet pan with parchment paper and have a clean towel handy for covering the dumplings once filled to prevent them from drying out. Have a small bowl of water handy for sealing the dumplings closed.

For each dumpling, put about 1½ tablespoons filling in the center of the wrapper. Dip a finger into the water and trace the edge of one side of the circle. Fold the wrapper over the filling, creating a half-moon shape, then use your fingers to pleat the edges closed. (If this is too hard, then simply press the edges together to seal.) Put the dumplings on the lined pan as you finish and cover with the towel. Repeat until you have used up all of the filling.

To pan-fry the dumplings, work in batches. In the large skillet over medium heat, add enough oil to completely coat the base of the pan (about 2 tablespoons). Once the oil shimmers, add 8 to 10 dumplings, spacing them out so they aren't touching. Cook until the bottoms are lightly browned, 3 to 4 minutes. Carefully add ¼ cup water to the pan (the oil will splatter) and cover with a lid. Cook until the water has mostly evaporated, then remove the lid and continue cooking off the remaining water until the wrapper is translucent and the dumpling bottoms are deeply browned and crispy, 3 to 4 minutes.

To serve:

Transfer the cooked dumplings to a serving plate and repeat this process until you've cooked all the dumplings you want for the meal. Serve immediately with the dipping sauce.