Dice the shallots, grate the ginger, slice the cabbage, mince 3 of the garlic cloves, remove the stems and dice the mushrooms, scallions, and water chestnuts.
Heat 1 tablespoon of the oil in a large frying pan over medium-high heat. Add the shallots, 2 teaspoons of the ginger, and the garlic. Cook for 5 minutes, then add the cabbage and mushrooms, and cook for 10 minutes on medium heat.
Then, add the water chestnuts, carrots, and peas, and cook for about 3 minutes, or until the peas are warmed through. Transfer the mixture to a bowl, and add 2 tablespoons of soy sauce, the sesame oil, and half of the scallions.
While the filling is cooking, prepare the wrappers. If you are using a square wrapper, place a bowl that is almost as big as the square upside down on the wrapper. Then, take a sharp paring knife, and trace around the bowl to create a round wrapper. If you have purchased round wrappers, you can skip this step.
Place about 2 tablespoons of the vegetable mixture in the center of the wrapper. Wet the edge of the wrapper with water, fold the wrapper's edge over to create a half moon, then pinch to seal, and pleat the edges tightly.
Heat 1 tablespoon of oil in a large frying pan over medium-high heat. Once hot, add 5 to 6 potstickers, or however many will fit in your pan. Lower the heat to low, and cook for 4 minutes. Then, add 3 to 4 tablespoons of water to the pan, cover, and steam the potstickers for 8 minutes. Repeat the process with the remaining potstickers.
While those are cooking, make the sauce by combining the remaining ¼ cup soy sauce, rice vinegar, the remaining ginger, 2 crushed garlic cloves, the remaining scallions, and the red pepper flakes. Serve the potstickers with the sauce.