Heat vegetable oil in a large Dutch oven.

Sauté the chopped onions and minced garlic until softened.

Add diced carrots and sliced celery to the pot and cook for about 10 minutes, stirring occasionally.

Pour in beef broth, chicken broth, and water.

Add barley to the pot.

Cover the Dutch oven and bring the mixture to a boil.

Stir in Worcestershire sauce, dried thyme, salt, and pepper.

Add the cooked cubed roast beef to the soup.

Stir in demi-glace or au jus mix.

Reduce the heat to low, cover, and simmer for 30-45 minutes, or until the vegetables and barley are tender.