Add the onion, garlic, celery, carrots to the pot and sauté until tender about 5-7 minutes. Next, add the mushrooms and thyme until the mushrooms render their juice and begin to brown. Stir in the tomatoes, beef and chicken broths, water, barley, and salt and pepper. Return the filet to the pot and bring to a boil for 1 minute. Simmer on low heat for 45 minutes before serving.