Pat short ribs dry with paper towels and season generously with salt and pepper on all sides.
Set Instant Pot to sauté mode and heat olive oil. Working in batches, sear the short ribs on all sides until deeply browned (about 3-4 minutes per side). Remove and set aside.
Add onion, carrots, and celery to the pot. Cook for 5 minutes, stirring occasionally, until vegetables begin to soften.
Add garlic and tomato paste, stirring for 1 minute until fragrant.
Pour in red wine and scrape up all the browned bits from the bottom of the pot. Let it simmer for 2 minutes.
Add beef broth, thyme, bay leaves, and Worcestershire sauce. Return the short ribs to the pot, nestling them into the liquid.
Close the lid, set valve to sealing, and cook on high pressure for 45 minutes.
Allow natural pressure release for 15 minutes, then quick release remaining pressure.
Carefully remove short ribs to a serving platter. Remove bay leaves and thyme stems. For a thicker sauce, set to sauté mode and simmer the sauce for 5-10 minutes. Spoon sauce and vegetables over the ribs, garnish with fresh parsley, and serve immediately.