Pat meat dry with paper towels to remove any excess moisture and transfer to a bowl. Sprinkle with flour and toss well to coat. Set aside. Heat a tablespoon of the olive oil in a large Dutch oven over medium-high heat. Stir onion into hot oil and cook for 5 minutes, until wilted and brown on edges. Add garlic and continue cooking for 2 minutes, stirring frequently. Transfer onion and garlic to a bowl and set aside.
Preheat remaining tablespoon of oil in the same pot. Add beef in a single layer and brown on all sides, stirring occasionally, 6 to 8 minutes. If pan is too small to fit all of the beef in one batch, simply transfer cooked beef to onion bowl and repeat with remaining beef. When beef has a browned crust, stir in beef broth, water, cooked onion and garlic, carrot, celery, barley, pepper and salt.
Bring liquid to a brisk simmer. Tie ends of fresh herbs together with a sturdy parsley stem or a piece of kitchen twine. Immerse herb bouquet in simmering broth and cook uncovered until barley and meat are tender and stew has thickened, 25 to 30 minutes.