Heat the 2 tablespoons oil in your wok over medium heat. Add the ginger and let it cook for about a minute until fragrant. Then turn up the heat to high and add the chicken. Keep stirring until the chicken is browned, and add the soaked shiitake and wood ear mushrooms. Keep stirring for another couple minutes.
Then add cooking wine, sugar, soy sauce, and dark soy sauce; mix everything well. Lastly, add 1 to 1 ¼ cup of the water you used to soak the mushrooms. Bring the liquid to a boil, cover the wok, and simmer over low heat for about 45 minutes, or until the sauce is thick and gooey. Make sure to stir occasionally, and remember to keep the heat low and add more water if you like a lot of sauce.
Finally, stir in the scallions until they're wilted. Serve!