Season beef with 1/2 teaspoon salt and pepper. Heat oil using the saute setting of a 6-quart electric pressure cooker and brown beef for 4 minutes per side, working in 2 batches if needed; transfer to a plate.
Cook onion in the cooker for 4 minutes, then stir in garlic for 30 seconds. Pour in broth and scrape the bottom completely clean before adding beef, bay leaf and thyme.
Lock the lid and pressure-cook on high for 50 minutes, allowing about 15 minutes to reach pressure. Let pressure release naturally for 15 minutes, then release any remaining pressure according to the cooker instructions.
Meanwhile, bring barley and its water to a boil in a saucepan. Cover partly and simmer for 50 to 65 minutes until tender but chewy, then drain thoroughly.
Transfer beef to a board and discard bay leaf. Add turnips and leeks to the cooker broth and simmer uncovered on the saute setting for 12 to 15 minutes until tender.
Discard beef bones and tough connective pieces, then pull the meat into short pieces. Return meat and drained barley to the broth with remaining salt and vinegar, simmer for 3 minutes and serve.