Wash 1½ cups of dried shiitake mushrooms a couple of times and rinse thoroughly. Soak them in 8 cups of water in a soup pot for at least 3 hours or overnight. After soaking, cut the stems and return the mushrooms to the pot of soaking water.
Add 2 tablespoons of dried goji berries and 6 pieces of dried red Chinese dates to the soup pot (no need to soak these beforehand). Bring the mixture to a boil over high heat, then immediately lower the heat to a simmer.
While the soup is simmering, wash 1 whole chicken (about 3 lbs) and pat it dry with a paper towel. Trim and set aside the chicken breasts for another dish. Cut the remaining parts of the chicken into large pieces and set aside.
After the soup has simmered for about 30 minutes, heat a wok over medium-high heat until it just begins to smoke. Reduce the heat to medium, then add 1 tablespoon of vegetable oil and 1 piece of sliced ginger. Cook for 1–2 minutes until fragrant. Swirl the oil to coat the wok, then spread the chicken pieces in a single layer. Lightly brown them on all sides, stirring occasionally, until most pieces are cooked through. Turn off the heat.
Add the browned chicken to the soup pot. Deglaze the wok with ½ cup of water, then pour the liquid into the soup pot as well. Add 3 tablespoons of Shaoxing wine, cover, and simmer over medium heat for another 30 minutes.
Season the soup with 2 teaspoons of salt, adjusting to taste. Garnish with 4 stalks of chopped green onion right before serving.