In a Dutch Oven or large stock pot, heat 2 tablespoons of olive oil over medium heat.
Working in batches, add some beef to the pot and season with salt and pepper. I cook about 1/4 of the meat at a time. It takes about 5-8 minutes to brown each batch. Do not drain the grease between batches.
As each batch cooks, set the meat aside on a plate and loosely cover it with foil. Do not remove the stuck brown bits from the bottom as this will add flavor later. Once all the meat is cooked, drain out the excess grease.
Add another 2 tablespoons of olive oil ad add the onions, celery, and carrots and season with salt and pepper. Cook until soft, about 8-10 minutes. Add the mushrooms about halfway through.
Add the garlic and stir it in. Cook for another 2 minutes.
Stir in the tomato paste with the vegetables. Allow the tomato paste to cook about 2-3 minutes. This will sweeten it up and eliminate the bitterness form the paste.
Pour in the red wine and stir. Use a wooden spoon to scrape the bits off the bottom of the pot.
Add in the beef stock and the cooked beef with the juices from the plate and stir.
Tie the fresh parley, fresh thyme, and bay leaves together using cooking twine, or tie them in cheese cloth. Add the bundle and season with salt and pepper.
Bring the soup to a boil and then reduce it to a simmer. Cover and allow the soup to simmer for 1 1/2 hour.
Add the barley and stir it in with the soup. Taste to see if you need to adjust the seasoning. Be careful not to over salt. Cover the pot again and cook for another 30 minutes.
After the 30 minutes, test to make sure the barley is soft. If it's not, continue cooking at 10 minute intervals. Keep in mind that the barley will continue to absorb the liquid after the soup is removed from the heat. You're looking for the barley to be just soft without any crunch, but not mushy.
When the soup is finished cooking, remove the herb bundle.