Pat beef cubes dry with paper towels. Heat 1 tablespoon olive oil in a large Dutch oven over medium-high heat. Working in two batches to avoid crowding, sear beef on all sides until deeply browned, about 3-4 minutes per batch. Transfer browned beef to a plate.

In the same pot, reduce heat to medium and add the remaining 1 tablespoon olive oil. Add onion, carrots, and celery. Cook, stirring occasionally, until vegetables begin to soften, about 5 minutes. Add garlic and tomato paste; cook for 1 minute more until fragrant.

Pour in a splash of the beef broth and scrape up any remaining browned bits. Return the beef and any accumulated juices to the pot. Add remaining broth, bay leaves, thyme, salt, and pepper. Bring to a boil, then reduce heat to low, cover, and simmer gently for 1 hour, stirring occasionally.

Stir in rinsed pearl barley. Continue to simmer, covered, for another 40-45 minutes, or until beef is fork-tender (internal temperature of at least 145°F/63°C) and barley is cooked through but still slightly chewy. Remove bay leaves and adjust seasoning.

Ladle soup into bowls, sprinkle with fresh parsley, and serve immediately with crusty bread.