These unique dumplings are like tiny omelettes cooked in a ladle directly over a burner.
In a large saucepan, combine stock, 1 knob of ginger cut into 3 slices, and rice wine. Bring to a boil, reduce heat to low, and simmer for 30 minutes. Remove from heat, strain and discard solids; set aside.
Place all the mushrooms in a bowl; cover with 2 cups very hot water. Soak until soft, about 20 minutes. Drain, discard the liquid, and remove and discard the stems; set aside.
Grate the other knob of ginger to obtain 1 teaspoon and combine it with the pork, 1 tablespoon of the egg mixture, cornstarch, salt, 1/4 teaspoon vegetable oil, sugar, scallion, and fish sauce and set aside.
Heat 1/2 teaspoon oil in a large soup ladle over a medium flame. Place about 1 tablespoon of the beaten egg in the ladle and swirl it, making a 3-inch circle, until the edges are set and the center is still wet. Use chopsticks to place about 1/4 teaspoon of pork filling in the center. Fold one side over, making a half circle. Use the blunt end of the chopsticks to gently press the edges together. Repeat until all the eggs and filling are used up. You should have 16 dumplings.
Pour broth into a large saucepan and add the mushrooms and all of the remaining ingredients. Place dumplings on the top. Bring broth to a boil, reduce heat to low, and simmer for 10 minutes. Serve immediately.