To begin, lightly dust beef cubes with flour. Heat oil in a large soup pot over medium-high heat. Brown the beef in batches until well-seared on all sides. Remove and set aside. Transition to cooking vegetables.
In the same pot, add onion, carrot, celery, and garlic. Cook for 5 minutes until softened and aromatic, scraping up browned bits from the base. Move to adding beef stock.
Return the beef to the pot. Stir in the rinsed pearl barley, then pour in beef stock. Add bay leaves, thyme, salt, and pepper. Bring to a gentle boil. Prepare to simmer.
Reduce the heat to low, cover loosely, and simmer for 45 minutes. Stir occasionally to prevent sticking. Transition to adding potatoes.
Stir in diced potatoes and continue simmering for another 20–25 minutes until potatoes and barley are tender. Move to final adjustments.
Taste the soup and adjust with more salt or pepper as needed. Remove bay leaves before serving. Proceed to garnishing.
Ladle the soup into bowls, garnish with chopped parsley, and serve with crusty bread. Presentation tip: serve in warmed bowls to keep the soup hot for longer.