Season beef with 1/2 teaspoon salt and pepper. Heat oil on sauté in a 6-quart electric pressure cooker. Brown beef 4 minutes per side, in 2 batches if needed. Transfer to a plate.
Cook onion in the cooker 4 minutes; stir in garlic for 30 seconds. Add broth; scrape bottom completely clean. Add beef, bay leaf and thyme.
Lock lid. Cook on high pressure 50 minutes, plus about 15 minutes to reach pressure. Release naturally 15 minutes; release remaining pressure following the cooker's instructions.
Meanwhile, boil barley and its water in a saucepan. Partly cover; simmer 50–65 minutes until tender but chewy. Drain well.
Transfer beef to a board; discard bay leaf. Add turnips and leeks to broth. Simmer uncovered on sauté 12–15 minutes, until tender.
Discard bones and tough connective tissue; pull beef into short pieces. Return beef and barley to broth. Add remaining salt and vinegar; simmer 3 minutes.