Rinse the dried shiitake and wood ear mushrooms, then soak them in hot water for at least 30 minutes until softened and plump. Once softened, squeeze out any excess water. Slice the shiitake, and if the wood ear mushrooms are large, cut them into bite-sized pieces. Reserve 1 tablespoon of the mushroom soaking liquid for the marinade.
Debone the chicken thighs and cut them into roughly ½-inch thick, bite-sized pieces.
In a bowl, combine the chicken with all the marinade ingredients and mix well. Add the sliced mushrooms and ginger, then mix everything together until evenly coated. Marinate for at least 15 minutes, or longer if you have time.
Transfer the marinated chicken and mushrooms to a shallow heatproof dish and spread everything out into an even layer so it cooks evenly.
Place a steaming rack in a deep wok and add about 2 inches of hot water. Put the plate of chicken on the rack, cover with a lid, and turn heat to high. Once the water starts to boil, steam for 12–15 minutes, or until the chicken is cooked through and tender.
Garnish with chopped green onions and serve hot with rice.
