Bring water or stock to a boil in a 4-quart soup pot. Reduce to a simmer, then add the barley. Cover and simmer until tender, around 40 minutes.

Heat the oil in a large, heavy frying pan, and sauté the onions, carrots, and dill weed. A few minutes later, add the celery. When browned and cooked nicely, add to soup pot. Sauté mushrooms in same pan quickly on high heat, until lightly cooked, then add them to the soup pot.

Let simmer 30 minutes covered. Add salt, pepper, tamari, and more water or stock as needed. The barley will continue to absorb water, making the soup thick. Before serving, add parsley.