Heat oil in a large Dutch oven over medium-high until shimmering. Toss together beef and ¾ teaspoon of the salt in a large bowl.

Working in 2 batches, add beef to hot oil, and cook, turning once, until browned on 2 sides, 6 to 8 minutes per batch. Using a slotted spoon, transfer beef to a medium bowl; set aside. (Do not wipe Dutch oven clean.)

Add onion, carrots, celery, and bell pepper to Dutch oven, reduce heat to medium, and cook, stirring occasionally, until onion is softened and translucent, 3 to 5 minutes.

Add garlic, and cook until fragrant, about 1 minute. Stir in tomato paste, and cook, stirring often, until color turns dark red, 1 to 2 minutes. Transfer to a medium bowl, and set aside.

Add chicken stock to Dutch oven, and bring to a simmer over high. Meanwhile, place thyme, bay leaves and peppercorns in a small cheesecloth sachet, draw strings together to close bag, and place sachet in chicken stock.

Add beef and remaining 2 teaspoons salt to chicken stock; reduce heat to medium, and bring to a simmer. Cover, reduce heat to medium-low, and gently simmer, occasionally skimming any foam that rises to surface, about 1 hour.

Stir in barley, and cook, covered, stirring occasionally, until barley is plump and almost doubled, about 30 minutes.

Stir in onion mixture; cook, covered, until barley is soft and vegetables are tender but still holding their shape, 30 to 40 minutes. Carefully remove herb sachet; discard. Garnish with parsley, and serve hot.