Season the short ribs generously with salt and pepper to taste. Select the Sauté button on the Instant Pot and add the olive oil. Add as many short ribs to the pot as you can without overcrowding (it will take two batches) and brown each side for 2-3 minutes. Flip the short ribs when they release easily. Once browned, remove to a plate and set aside.

Add the onion, carrot and celery to the pot and sauté until softened, about 4 minutes. Add the garlic and cook 30 seconds. Add the red wine and deglaze the pan, using a wooden spoon to scrape up the brown bits from the bottom of the pot. Cook for 1 minute to cook off some of the alcohol, then add the tomato paste, balsamic vinegar and beef stock and stir well. Add the bay leaf and 2 sprigs rosemary, then add the short ribs back to the pot along with any accumulated juices on the plate. Secure the lid, close the venting valve and cook for 45 minutes at High Pressure. Naturally release the pressure for 10-15 minutes and quick release the pressure from there as necessary, then remove the lid when safe to do so.

Discard the bay leaf and rosemary, then transfer the short ribs to a plate. Using a slotted spoon, remove the vegetables from the pot and place in a bowl or along with the short ribs. Skim off any pools of fat on top of the sauce.

Place the Instant Pot on Sauté mode and combine the cornstarch with 1.5 tablespoons water. Add it to the pot and cook, stirring constantly, until the sauce has thickened to the desired consistency, about 1-2 minutes. Turn off the heat and adjust the seasoning as necessary.