Season beef cubes generously with salt and pepper. Set Instant Pot to Sauté mode and heat 1 tablespoon oil until shimmering.
Brown beef in batches for 2-3 minutes per side until deeply golden. Transfer to a plate and repeat with remaining beef, adding more oil as needed.
Add remaining oil, onion, and garlic to the pot. Sauté for 3-4 minutes until softened, scraping up any browned bits from the bottom.
Stir in tomato paste and cook for 1 minute. Add wine and deglaze the pot, scraping the bottom thoroughly to prevent burn warning.
Return beef to pot with beef broth, Worcestershire sauce, thyme, and bay leaves. Stir to combine, ensuring beef is mostly submerged.
Lock lid, set valve to Sealing, and pressure cook on High for 20 minutes. Allow 10-minute natural release, then quick release remaining pressure.
Add potatoes, carrots, and celery to the pot. Lock lid again and pressure cook on High for 5 minutes, then quick release pressure.
Mix flour and cold water until smooth. Set pot to Sauté and stir in slurry. Simmer for 3-5 minutes until thickened to desired consistency.
Remove bay leaves and taste for seasoning, adjusting salt and pepper as needed. Garnish with fresh parsley and serve hot with crusty bread.