Season steak generously with black pepper. Heat 2 teaspoons oil in a Dutch oven over medium high heat. Add the steak in 2 separate batches and cook, stirring often, until browned on all sides, about 2 minutes. Transfer to a bowl with drippings.

Add the remaining 2 teaspoons oil, onion, celery, carrots, mushrooms and garlic to the pot and cook, stirring, until beginning to soften, about 2- 4 minutes. Add the tomato paste and thyme and cook, stirring, until the vegetables are coated with the tomato paste and are beginning to brown, 1-2 minutes.

Add the broth, and bring to a boil. Add barley & steak with any drippings and reduce the heat to maintain a simmer; cook until the barley is tender, about 15 minutes. Remove from the heat; stir in parsley & balsamic vinegar. Taste to see if more salt and pepper are needed. Serve. When reheating leftovers, add more broth if necessary.