Season all sides of the short ribs with kosher salt and black pepper.
Add olive oil to the Instant Pot and set to the "saute" setting.
When the oil is hot add in the short ribs (I do about 3 or 4 at a time) and brown on all sides. This should take about 7-8 minutes per batch.
When the ribs are browned set aside and add the carrots and onions to the pot. If there is not enough oil drizzle in a little so the vegetables don't stick. Cook for about 10 minutes or until the carrots just start to soften and the onions are translucent.
Add the garlic, rosemary, thyme and tomato paste and stir to combine. Cook for about 30 seconds or just until the garlic is fragrant.
Pour in the red wine and scrape the bottom of the pan so you get up any brown bits that may have happened on the bottom of the pot.
Turn off the saute setting.
Add the short ribs back to the pot, secure the lid, make sure the nozzle is placed to "seal" and cook on manual high pressure or stew setting for 45 minutes.
When the ribs have finished cooking manually release the pressure and remove the lid when unlocked.
Carefully remove the short ribs from the pot and skim off any fat at the top of the liquid in the pot. I like to use a soup ladle to help take off as much fat as possible. This takes about 5 minutes.
Put the Instant Pot on saute mode.
In a small bowl mix together cornstarch and cold water. When combined add to the Instant Pot liquid and let the mixture cook down a bit while it thickens up. Make sure to stir the liquid while it's cooking. When the liquid is thick and looks like gravy turn off the heat.
Add the short ribs back to the pot so they stay warm.
Serve with mashed potatoes or pasta and top with 1 or 2 short ribs and a spoonful of gravy and vegetables.