In a large saucepan, heat 1 tablespoon of the oil over medium heat. Add onion, cover, and cook until soft, about 8 minutes. Stir in broth, increase heat to high, and bring to a boil. Reduce heat to medium, stir in barley, and cook, covered, for 20 minutes.
While onion is cooking, season steak with pepper. Heat remaining 1 tablespoon oil in a large skillet over high heat. Add half of the steak, and cook until browned, about 3 minutes. Transfer cooked steak to a bowl and set aside. Add remaining steak to skillet and cook until browned, then add garlic and cook 1 minute more.
When barley is cooked, stir steak and frozen vegetables into soup. Simmer 5 minutes.