Place dried porcini mushrooms in a small bowl and pour in 1 cup boiling water. Let stand until softened, about 40 minutes. Drain mushrooms, reserving liquid and coarsely chop. Strain liquid and set aside.
Meanwhile, in a heavy saucepan over medium heat, heat oil 1 minute. Add onion, garlic and ginger, and cook, stirring frequently, about 7 minutes. Stir in carrot and bell pepper and cook, stirring occasionally, until tender, about 5 minutes.
Add reserved mushrooms, 2 tablespoons mushroom liquid, and shiitake and button mushrooms, and sauté 5 minutes or until tender. Stir in tomatoes and barley.
Add remaining mushroom liquid, broth, salt and rosemary, and bring to boil. Reduce heat to medium low, cover and simmer 45 minutes or until barley is tender.