Pre-cook the beef: Combine the water, beef, red wine vinegar and salt in a large pot. Bring to a boil, then reduce heat to low and gently simmer for 1 1/2 hours. Drain, discarding liquid and reserving the beef. Allow to cool slightly, then chop into desired size for soup (or make ahead and refrigerate until needed).
For the soup: In a large soup pot, heat the oil over medium heat. Add the garlic, onion, celery and carrots to the pot and cook, stirring, for 6-7 minutes. Add red wine to the pot and allow to cook until mostly evaporated. Add the tomato paste and stir in. Cook the tomato paste with the vegetables for about 1 minute. Add the beef broth, cooked beef pieces, pearl barley and bay leaf. Stir to combine.
Bring mixture to a boil, then reduce heat to medium low and allow soup to simmer gently for 60-75 minutes. Watch the soup as it cooks and stir regularly. As the barley cooks, it will absorb the liquid. You may find that you need to add additional beef broth to the pot as the soup cooks. You don't want the soup to get too dry or the barley will sink to the bottom of the pot and may scorch. Ideally, add a bit of broth more often, rather than adding a lot all at one time, so you don't end up with too much broth in the pot and a thinner soap than you want.
Taste test the soup to make sure the barley and carrots are tender. If not, cook a little bit longer. If soup is too thick, add a bit more broth at the end of cooking to thin it as desired. Stir in the Worcestershire sauce and parsley. Taste soup for seasoning and add additional salt and some freshly ground pepper, to taste.
Notes
Be sure to read the Ingredient Notes above the Recipe Card for some substitution tips. You'll also find Step-by-Step Photos and Cook's Notes there, as well.