Season boneless short ribs with 1 ½ teaspoons salt.
Turn on the instant pot and set to "Sauté" and adjust to more high heat.
Add vegetable oil and heat until it shimmers. Working in batches, add boneless beef short ribs and cook for about 3 minutes on each side or until browned. Remove from instant pot and set aside.
Add dry red wine to instant pot. Stir and scraping up any browned bits from the bottom of the instant pot. Bring the red wine to a boil and until it is reduced by 1/3 for about 1 minute. Add beef broth, garlic, onion, dried thyme, paprika, tomato paste, black pepper, salt and browned boneless beef short ribs to instant pot.
Set the instant pot to "manual" and cook at high pressure for about 30 minutes. When cooking is complete, use a natural release to depressurize.
Add chopped carrots to pot and cook at high pressure for 2 minutes. When cooking is complete, use a quick release to depressurize.
To thicker the sauce, mix 2 tablespoons of water with 1 tablespoon flour. 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 noodle, polenta or on a bun.