Soak the dried mushrooms in hot water until softened, about 1 hour. Drain the water, discard the stem, and finely chop the mushroom caps.
In a large bowl, combine the mushrooms, pork, water chestnuts, green onions, fresh ginger, soy sauce, cornstarch, wine, sesame oil, sugar, pepper and egg white. Mix well.
Line bamboo steamer trays with parchment paper.
Spoon scant 1 tablespoon of filling onto middle of a dumpling skin. Gather the dumpling skin together and use your cupped hands to form the siu mai. If you have trouble getting the skin to stick together, you can brush the inside of the dumpling skin with a little bit of cornstarch slurry (1 tablespoon cornstarch + 3 tablespoons water). Top each siu mai with a bit of minced carrot.
Place dumplings into bamboo steamer, cover the dumplings with damp paper towel or plastic wrap until ready to cook - this will prevent the dumplings from drying out). When ready to cook, remember to remove the plastic wrap or paper towels. Steam for 8 minutes.