Brown the Beef: In a large pot, heat the olive oil over medium-high heat. Add the beef stew meat and brown on all sides. Remove the beef from the pot and set aside.
Sauté the Vegetables: In the same pot, add the chopped onion, minced garlic, sliced carrots, celery, and mushrooms. Sauté for 5-7 minutes, until the vegetables are softened.
Add the Broth and Barley: Return the browned beef to the pot. Add the beef broth, diced tomatoes (with juice), tomato paste, pearl barley, thyme, rosemary, and bay leaves. Stir to combine.
Simmer: Bring the soup to a boil, then reduce the heat to low. Cover and simmer for 1-1.5 hours, or until the beef and barley are tender. Stir occasionally.
Season: Remove the bay leaves. Season the soup with salt and pepper to taste.
Serve: Ladle the soup into bowls and garnish with freshly chopped parsley.