Heat oil in a large Dutch oven over medium-high; brown beef all over in uncrowded batches, about 8 minutes total.
Remove beef; set aside. Cook onion, carrots, and celery in pot about 5 minutes until softened.
Stir in garlic and tomato paste; cook 1 minute until fragrant.
Return beef; add barley, broth, water, bay leaves, thyme, salt, and pepper. Bring to boil.
Reduce heat to low; cover and simmer 1.5 to 2 hours until beef is tender and barley cooked through, stirring occasionally.
Remove bay leaves; adjust seasoning to taste and garnish with parsley before serving.