Remove the short ribs from the refrigerator 20-30 minutes before cooking. Pat them thoroughly dry with paper towels, then season generously on all sides with kosher salt and black pepper.
Press Saute (High) on the Instant Pot and heat the olive oil for 2-3 minutes until hot. Sear the short ribs in batches, bone-side up, for 3-4 minutes per meaty side until deeply browned, then transfer to a plate.
Add the onion, garlic, carrots, and celery to the pot and cook for 3-4 minutes until softened. Stir in the tomato paste and cook for 1-2 more minutes until it darkens slightly.
Pour in the red wine and scrape up all browned bits from the bottom of the pot. Simmer for 2 minutes, then add the beef broth, Worcestershire sauce, and balsamic vinegar and stir to combine.
Nestle the seared ribs back into the pot bone-side up and tuck in the rosemary and thyme sprigs. Seal the lid, set the valve to Sealing, and cook on High Pressure for 45 minutes.
Allow the pressure to naturally release for 15 minutes, then carefully switch the valve to Venting to release any remaining pressure. Remove the lid once the float valve has fully dropped.
Carefully transfer the short ribs to a platter using tongs and discard the herb sprigs. Strain the braising liquid through a fine-mesh strainer and skim or separate the fat from the surface.
Return the strained liquid to the Instant Pot on Saute mode or to a saucepan over medium-high heat. Whisk together the cornstarch and cold water, pour into the simmering sauce, and cook for 2-3 minutes until glossy and thickened.
Spoon the sauce generously over the short ribs, garnish with freshly chopped parsley, and serve immediately over mashed potatoes, egg noodles, or creamy polenta.