Brown the short ribs: Season boneless short ribs with 1 ½ teaspoon of kosher salt. Select the "Sauté" setting on high heat. When the IP displays “Hot”, heat the oil. Working in batches, add boneless beef short ribs. Cook for about 3 minutes on each side or until browned. Set aside.
Deglaze: Add dry red wine. Stir and scrape up any browned bits from the bottom of the instant pot. Bring the red wine to a boil and cook until it is reduced by ⅓ for about 1 minute.
Pressure Cook: Add beef broth, garlic, onion, dried thyme, paprika, tomato paste, black pepper, salt and browned boneless beef short ribs to the instant pot.Secure the lid and select the "Manual" setting. Adjust time to 30 minutes on high pressure. When cooking is done, let the IP release pressure naturally.
Pressure Cook the Carrots: Open the lid. Add chopped carrots then secure the lid again. Select the "Manual" setting, adjust time to 2 minutes on high pressure. When cooking is completed, quick release to depressurize.
To Thicken the Sauce: In a small bowl, mix in 1 tablespoon of water with 1 tablespoon of corn starch. Set the instant pot to "sauté", add the flour mixture and let stew simmer until thickened. Adjust seasoning with salt and pepper if needed.
Turn off the instant pot and sprinkle the stew with some fresh parsley. Serve immediately with egg noodles, polenta or on a bun.