Season steak with 1/4 teaspoon pepper. Heat 2 teaspoons oil in a Dutch oven over medium heat. Add the steak and cook, stirring often, until browned on all sides, about 2 minutes. Transfer to a bowl.

Add the remaining 2 teaspoons oil, onion and celery to the pot and cook, stirring, until beginning to soften, about 2 minutes. Add carrot and cook, stirring, for 2 minutes more. Add tomato paste and thyme and cook, stirring, until the vegetables are coated with the tomato paste and are beginning to brown, 1 to 2 minutes.

Add barley, broth, water, salt and the remaining 1/4 teaspoon pepper; bring to a simmer. Reduce heat to maintain a simmer; cook until the barley is tender, about 15 minutes. Return the beef and any accumulated juice to the pot and heat through, 1 to 2 minutes. Remove from the heat; stir in vinegar to taste.