In a large, heavy-bottomed soup pot, heat the oil and brown the beef in small batches, seasoning each batch with salt and pepper. Use a slotted spoon to transfer the browned meat to a bowl, leaving as much fat in the pot as possible.
Once all the meat has been browned and removed, add the onion, celery, carrot, and parsley to the pot, cover and cook over medium heat, stirring occasionally for about 5 minutes, until the vegetables are soft.
Return the beef to the pot along with any juices that have collected in the bowl. Add the broth, barley, tomatoes (with their liquid), Worcestershire sauce, bay leaves, and thyme.
Bring the soup to a boil, then lower the heat, put the cover ajar, and simmer 1-1/2 hours, stirring occasionally and adding water if the soup becomes too thick. Skim any fat that has risen to the surface of the soup, discard the bay leaves, and season with salt and pepper to taste.
Ladle into bowls and garnish with the remaining parsley.