Heat the olive oil in a large heavy-bottomed pot or Dutch oven over medium-high heat. Add the beef chunks and sear until browned on all sides, about 5 to 7 minutes. Work in batches if necessary to avoid crowding the pan.
Add the diced onion, carrots, and celery to the pot with the beef. Cook for 5 minutes until the vegetables begin to soften. Stir in the minced garlic and tomato paste, and cook for 1 additional minute.
Pour in the beef broth and scrape the bottom of the pot with a wooden spoon to release any browned bits. Stir in the pearl barley, dried thyme, salt, and black pepper.
Bring the soup to a gentle boil, then reduce the heat to low. Cover the pot and simmer for 1.5 to 2 hours, or until the beef and barley are completely tender. Stir occasionally to ensure the barley does not stick to the bottom.
Remove the pot from the heat and stir in the fresh chopped parsley. Taste and adjust seasoning if necessary before serving.
Crockpot Alternative: Sear the beef in oil on the stovetop, then transfer it and all remaining ingredients to a slow cooker. Cook on LOW for 7 to 8 hours or HIGH for 4 to 5 hours until the beef is very tender [1.4].