Turn on the Instant Pot to Saute and add 2 tablespoons of oil to the pot. Sautee the carrots and onions for about 4 minutes. Add the garlic and cook for 1 more minute, then transfer the veggies to a bowl.
Dry the short ribs with a paper towel and then season them all over with salt. Spread the flour out on a plate and lightly coat the ribs in flour.
Add another 2 tablespoons of oil to the pot. Use tongs to place 4 short ribs into the pot and brown all sides, about 1-2 minutes searing per side. Transfer to a plate once browned and repeat with the remaining oil and ribs. *If the ribs are very thick, be sure to brown the ends as well.
Pour in the wine to deglaze and scrape up all the brown bits on the bottom of the pot. Allow the wine to cook down for about 2 minutes. Then add the beef broth, and tomato paste and mix to combine.
Place the seared short ribs and cooked vegetables back into the Instant Pot and top with sprigs of thyme.
Cover, lock the lid, set the vent to sealing, and cook on Manual for 45 minutes. Once the cooking time is up, allow a 10-minute natural release before quick releasing any remaining pressure.
Using tongs, carefully transfer the ribs to a plate and use a slotted spoon to remove the vegetables from the cooking liquid.
If you want to make gravy for your short ribs, turn the Instant Pot back to Saute. Stir together the cornstarch and ¼ cup of the cooking liquid from the Instant Pot until combined.
Pour the cornstarch slurry back into the Instant Pot. Whisk constantly while cooking down to your desired thickness, about 2-3 minutes (just enough to coat the back of a spoon).
Plate two short ribs with mashed potatoes and/or vegetables, and spoon some gravy over the ribs. SPrinkle with a little parsley before serving.