Step 1Place rice noodles in large bowl and cover with warm water. Place dried mushrooms in small container with tight-fitting lid, add warm water to top of container and cover. (Dried mushrooms float; placing them in covered container ensures that they will be submerged.) Soak noodles and mushrooms 20 minutes. Drain noodles in colander and set aside. Drain mushrooms, pat dry with paper towels, trim and discard stems and cut tops into thin strips.
Step 2Meanwhile, in 3 1/2 to 4-quart saucepan, bring broth to boil. Reduce heat to simmer, add ginger and carrot, and cook until carrot is crisp-tender, 12 to 15 minutes. Add soy sauce, ham, watercress, green onions, drained rice noodles and mushrooms. Stir to combine and heat through, 1 to 2 minutes. Ladle into warm soup bowls and serve immediately.