Prepare the beef: Pat the beef chuck dry with paper towels. Season all sides with salt and black pepper.
Heat the Dutch oven: Place a large Dutch oven over medium-high heat and add the olive oil.
Brown the beef: Add the beef in batches, making sure not to overcrowd the pot. Sear for about 2–3 minutes per side until deeply browned. Transfer the browned beef to a plate.
Sauté the vegetables: Reduce the heat to medium. Add the onion, carrots, and celery to the Dutch oven. Cook for 5–7 minutes until the vegetables begin to soften.
Add the garlic and tomato paste: Stir in the garlic and tomato paste. Cook for about 1 minute, stirring frequently, until fragrant.
Deglaze the pot: Pour in a small amount of the beef broth and scrape the bottom of the Dutch oven with a wooden spoon to loosen all the flavorful browned bits.
Build the stew: Return the browned beef to the Dutch oven. Add the remaining beef broth, Worcestershire sauce, thyme, and bay leaves. Stir well.
Simmer the beef: Bring the stew to a gentle simmer, then reduce the heat to low. Cover and cook for about 1½ hours, stirring occasionally, until the beef begins to become tender.
Add the barley: Stir in the pearl barley and optional mushrooms. Cover again and continue simmering for approximately 35–45 minutes, or until the barley is tender and the beef is fork-tender.
Adjust the consistency: If the stew is too thin, simmer uncovered for several minutes. For a thicker consistency, whisk 1 tablespoon of flour with a little cold water to make a smooth slurry, then stir it into the stew and simmer for a few minutes.
Finish the stew: Remove the bay leaves. Taste and adjust the salt and black pepper as needed. Stir in the fresh parsley.
Serve: Ladle the hot Beef and Barley Stew into bowls and serve with crusty bread, dinner rolls, or a simple green salad.