Put the shiitake mushrooms in a bowl and cover with the boiling water. Set aside to soften for about 20 minutes. Rub the mushrooms in the soaking liquid to remove any grit. Discard the stems and thinly slice the caps. Set the soaking liquid and the sliced caps aside.
In a medium bowl, stir together the egg white, cornstarch, salt, and 1 tablespoon of water. Add the chicken and stir well to coat. Set aside for 20 minutes.
Put the cellophane noodles in a bowl and cover with warm water. Set aside until pliable, about 10 minutes. Drain the noodles and set aside. In a small bowl, combine the wine, soy sauce, oyster sauce, peanut oil, sesame oil, garlic, and sugar.
In a large saucepan, combine 3 cups of water with the ginger and star anise. Slowly pour in the reserved mushroom liquid, stopping before you reach the grit at the bottom. Bring to a boil over high heat. Reduce the heat to low, cover and simmer for 10 minutes. Add the soy sauce mixture and increase the heat to moderately high.
Add the chicken and cook until opaque, stirring with a large fork to separate the strips. Add the shiitakes and the cellophane noodles. Using tongs, lift and stir the noodles until they become transparent, about 3 minutes. Stir in the Swiss chard and scallions and transfer to 4 large bowls. Season with white pepper and a few drops of chili oil and serve.