Special equipment: a steamer basket
Bring 1 cup water, the mushrooms and ginger slices to a boil in a small saucepan over high heat. Reduce the heat and simmer until the mushrooms are soft and the water is reduced by half, about 20 minutes. Remove the mushrooms and cut off the stems. Reserve the caps. Remove the ginger slices from the liquid and reserve the liquid.
Coarsely chop the mushroom caps, ginger slices, water chestnuts and cilantro in a food processor. Add the ground pork, cornstarch, soy sauce, sesame oil, sugar, pepper and reserved mushroom liquid. Blend well. Remove to a bowl. Filling may be made up to a day ahead and refrigerated, well covered.
Lay 24 dumpling skins on a clean work surface. Place 1 scant teaspoon of filling in the center of each circle. Gather the skins up around the filling, but do not enclose the top. Squeeze lightly in the center to form a waist. Pat down the filling to flatten the top. Dumplings should resemble a flower. Repeat in batches of 24.
Grease a flat plate with vegetable oil and place the finished dumplings on the plate to oil the bottoms. Place about 1/3 of the dumplings in each of three steamer baskets, arranging in the baskets in a single layer without touching. Stack the steamer baskets and steam the dumplings until firm, about 10 minutes. Serve with spicy dipping sauce.