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Season beef with salt and pepper. In a pressure cooker, heat 1 tablespoon (15ml) oil over high heat until lightly smoking. Working in batches if necessary, add beef and cook, turning occasionally, until well browned on all sides, about 5 minutes per side. Transfer to a large platter.
Add diced carrot, diced onion, and diced celery to pressure cooker and cook, stirring and scraping up any browned bits from the bottom, until lightly browned, about 6 minutes. Scrape vegetables into a heatproof bowl and set aside.
Add remaining 1 tablespoon (15ml) oil to pressure cooker and heat over medium-high heat until shimmering. Add remaining whole carrot, halved onion, and whole celery rib, along with garlic, and cook, stirring occasionally, until browned in spots, about 4 minutes. Add wine to pot and cook, scraping up any browned bits from bottom of pot, until wine comes to a simmer and alcohol smell cooks off, about 4 minutes.
Add stock, thyme, bay leaf, reserved beef and any accumulated juices, and barley to pressure cooker; the liquid should just cover all the other ingredients. Close cooker, bring to high pressure, and cook for 30 minutes. Release pressure using pressure release valve.
Remove beef, discard bones (they should fall right out), and cut meat into bite-size chunks. Return to pot. Discard thyme sprigs, large vegetable chunks and garlic cloves, and bay leaf. Stir in reserved diced vegetables and fish sauce, if using. Season with salt and pepper. Stir in peas and cook until just warmed through. Serve.