In a medium bowl, combine the dates and goji berries. Pour boiling water over the top, cover with aluminum foil, and set aside to soak for 20 minutes.
Add olive oil to a large Dutch oven, and heat over medium heat. When it shimmers, add the onions and cook until soft and translucent, about 5 minutes. Season with salt.
Increase the heat to medium-high, add the chicken, and cook, stirring, until lightly browned, 5 to 7 minutes.
Add the chiles, ginger, and garlic, and cook, stirring, until fragrant, about 5 minutes more.
Pour in the broth and soy sauce, increase the heat to high, and bring to a boil. Reduce the heat to low and simmer gently.
Drain the goji berries and red dates and add them, along with the shiitake mushrooms, to the broth.Simmer the soup, with the lid slightly ajar, for 25 to 30 minutes more, until the flavors have merged together.Serve and garnish with the chopped green onion.