Pat beef dry and season with salt and pepper. Heat olive oil in a large pot over medium-high heat and brown beef in batches until well-seared, about 4–5 minutes per batch.
Remove browned beef and set aside. Lower heat to medium, add a touch more oil if needed, then sauté diced onion until translucent, about 4 minutes.
Add minced garlic and tomato paste; cook 1 minute until fragrant.
Stir in sliced carrots and celery; cook 3–4 minutes to soften slightly.
Return beef to the pot, add rinsed pearl barley and pour in beef broth, scraping up browned bits from the bottom.
Add bay leaf and thyme; bring to a boil, then reduce heat to a gentle simmer.
Partially cover and simmer for about 50–60 minutes, stirring occasionally, until barley is tender and beef is fork-tender.
Taste and adjust seasoning with salt and pepper; remove bay leaf.
Stir in chopped parsley and let the soup rest 5 minutes before serving.
Serve hot with crusty bread or a green salad; garnish with extra parsley or a drizzle of olive oil.