Combine the boiling water and shiitake mushrooms in a bowl; cover and let stand 30 minutes. Drain mushrooms, reserving liquid. Discard mushroom stems; slice mushroom caps, and set aside.
Heat oil in large Dutch oven over medium-high heat. Add onion and next 8 ingredients (onion through bay leaves); sauté 3 minutes. Add 4 cups water and broth; bring to a boil. Cover, reduce heat, and simmer 35 minutes, stirring occasionally. Add shiitake mushrooms, fresh mushrooms, salt, and pepper; cover and simmer an additional 10 minutes.