Heat the oil in a large pot over medium-high heat. Season the beef with ½ teaspoon salt and ¼ teaspoon pepper. Working in 2 batches, cook the beef, turning often, until browned, 4 to 6 minutes; transfer to a plate.
Add the onion, carrots, celery, and garlic to the pot and cook, stirring often, until beginning to soften, 4 to 6 minutes.
Add the broth, tomatoes (with their juices), barley, bay leaf, thyme, 4 cups water, ¼ teaspoon each salt and pepper, and the browned beef (along with any accumulated juices). Bring to a boil, reduce heat, and simmer, covered, until the beef is tender, 1 hour to 1 hour, 15 minutes.
Adjust the consistency of the soup with more broth or water if desired. Stir in the parsley.
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