Pour enough warm water over the mushrooms in a medium bowl to cover them completely. Soak until softened, about 20 minutes. Drain. Discard the stems and chop the caps finely.
To prepare the seasonings: Stir the soy sauce, oyster-flavored sauce, dark soy sauce, sesame oil and sugar together in a small bowl until the sugar is dissolved.
To make the filling: Heat a wok over high heat until hot. Add the oil and swirl to coat the sides. Add the ground pork and ham and stir-fry until the pork is crumbly and cooked through, 1 1/2 to 2 minutes. Add the rice, bamboo shoots, water chestnuts, green onion, seasonings, and reserved mushrooms. Cook, stirring, until heated through, for about 1 minute. Remove the filling from the wok and let cool.
To make the dumplings: Place 1 tablespoon of the rice mixture in the center of a wrapper. (Keep remaining wrappers covered with a damp towel to prevent them from drying out). Gather up the wrapper around the filling, pleating it as you go to form an open-topped pouch. Carefully squeeze the sides of the dumpling about half way up to give the dumpling a 'waist.' Center a pea over the top of the dumpling. Repeat with the remaining dumplings, keeping the formed dumplings covered with a damp cloth while filling the remaining wrappers.
Pour enough water into a wok to reach about 2 inches up the sides and bring to a boil. Line the inside of a bamboo steamer with cabbage leaves or parchment paper and set it over the water (the steamer shouldn't touch the water). Place as many dumplings in the steamer as will fit without touching each other. Steam the dumplings until the wrapper is cooked and tender to the touch, 3 to 4 minutes. Serve with classic dim sum accoutrements like hot mustard, chili paste and soy sauce.