Place the dried mushrooms in a saucepan with the cold water and let soak 2-3 hours, or overnight. Remove mushrooms and finely dice, reserving the water.
Add the barley to the mushroom-soaking water and bring to a boil. Reduce heat, cover and simmer 30-40 minutes.
Meanwhile, heat the oil or butter and saute onion until transparent. Add the mushrooms and cook another 5-10 minutes. Add to the soup along with the potatoes and carrot. Season to taste and simmer 20 minutes or until potatoes are done.
Serve sprinkled with chopped parsley or dill and a spoonful of sour cream.