**Sear the Beef:** Heat olive oil in a large pot over medium-high heat. Season the beef with salt and pepper. Add the beef to the pot and sear until browned on all sides, about 5-7 minutes. Remove the beef and set aside.
**Sauté the Vegetables:** In the same pot, add the onion, carrots, and celery. Sauté for 5-7 minutes until softened. Stir in the garlic and cook for 1 minute.
**Add the Tomato Paste and Spices:** Stir in the tomato paste, thyme, and bay leaf, cooking for 1-2 minutes to develop flavor.
**Combine Ingredients:** Return the beef to the pot. Add the barley, beef broth, and optional water. Bring to a boil, then reduce heat to low and simmer, covered, for 45 minutes.
**Add Mushrooms (Optional):** Stir in the mushrooms during the last 15 minutes of cooking.
**Adjust Seasoning:** Remove the bay leaf. Taste the soup and adjust salt and pepper as needed.
**Garnish and Serve:** Serve hot, garnished with fresh parsley, alongside crusty bread or crackers.