Heat the olive oil in a large pot over medium-high heat. Add the beef stew meat and cook until browned on all sides.
Add the diced onions, garlic, carrots, and celery to the pot. Cook for about 5 minutes, until the vegetables are tender.
Stir in the tomato paste, thyme, and rosemary. Cook for another 2 minutes.
Pour in the beef broth and bring to a boil. Reduce heat and simmer for 1.5 hours.
Add the rinsed barley and continue to simmer for another 30 minutes, or until the barley is tender.
Season with salt and freshly ground black pepper to taste. Serve hot.