Soak dried shiitake mushrooms in 2 cups of boiling water for 20-30 minutes. Strain mushrooms and reserve liquid. Squeeze mushrooms to remove all the water and then dice.
Heat oil in a large pot over medium heat, add coarsely chopped leeks and garlic. Cook until softened.
Add chopped carrots, fresh shiitakes (stems removed, caps chopped), chopped white mushrooms and cook until softened. Season with salt and pepper.
Add chopped chicken and cook until no longer pink on the outside (about 5 minutes).
Add broth, barley, thyme and shiitake mushrooms & soaking liquid.
Simmer soup until the barley is tender, about 1 hour.