Pat the beef dry and season it with half the salt and pepper.
Heat the olive oil in a Dutch oven and brown the beef in batches; transfer to a plate.
Cook the onion, carrots, and celery for 6 minutes, then stir in the garlic and tomato paste for 1 minute.
Return the beef and its juices, then add the broth, barley, thyme, bay leaf, remaining salt, and pepper.
Bring to a boil, reduce to a gentle simmer, cover, and cook for 60 minutes.
Uncover and simmer for 20 to 30 minutes more, until the beef and barley are tender and the stew thickens.
Discard the bay leaf, adjust seasoning, and serve hot.