Heat olive oil in a large pot over medium heat. Add the beef and brown on all sides. Remove and set aside.
In the same pot, sauté the onions, carrots, and celery until softened. Stir in the garlic and tomato paste and cook for another minute.
Return the beef to the pot. Add the beef broth, bay leaves, thyme, salt, and black pepper. Bring to a simmer.
Reduce heat to low, cover, and let simmer for 1.5 to 2 hours until the beef is tender.
Stir in the barley and continue cooking for another 30 minutes until the grains are tender.
Remove the bay leaves, adjust seasoning if needed, and serve hot.