Heat oil in a large pot over medium-high heat. Season beef with 1/4 tsp of the salt and the black pepper and add to pot; sauté 5 minutes, turning once. Add onion and garlic; cook 3 minutes, stirring occasionally.
Add stock, 3 cups water, carrots and celery. Cover and simmer 60 minutes, stirring occasionally. Add tomatoes, mushrooms, barley, remaining 3/4 tsp of the salt and the thyme. Simmer 30 minutes, covered, stirring occasionally.
Stir in peas and simmer 2 minutes. Garnish with parsley, if desired.