Place the dried mushrooms in a bowl, bring 1 cup of water to a boil, then pour it over the dried mushrooms and let them soak for 30 minutes. Remove the mushrooms from the liquid, give them a squeeze to remove excess liquid, then chop them. Pour the soaking liquid through a fine mesh strainer and reserve. Meanwhile, trim the fresh mushrooms, removing the stems of the shiitakes completely, wipe them with a damp paper towel to remove any dirt, and coarsely chop them.

While the mushrooms are finish soaking, in large soup pot, heat the olive oil over medium heat, then add the leeks, carrots, and chopped fresh mushrooms, season with salt and pepper, and sauté for 8 minutes until the vegetables are starting to become tender, and any liquid the mushrooms have released evaporates. Let the mushrooms saute until they start to brown slightly. Add the chicken and barley, and sauté until the chicken is starting to take on some color, and everything is well combined with the oil and vegetables.

Add 6 cups of the broth, the reserved mushroom soaking liquid, and the chopped soaked dried mushrooms, raise the heat to medium high, and bring to a simmer. Reduce the heat to medium low, partially cover, and simmer the soup for 30 minutes. Then add oregano and half of the lemon zest, and continue to simmer for about another 30 minutes, until the barley is cooked and tender. Add up to 2 more cups of broth as needed/desired as the soup finishes cooking if it seems too thick. Serve hot, with a sprinkle of lemon zest and some oregano leaves over each serving if desired.