Take the short ribs out of the refrigerator and let them rest and warm up for about 30 minutes. Take them out of the package and pat them dry with paper towels.
Season them well with coarse salt and pepper on all four sides.
Slice onion, carrot, and celery and set aside.
Sear vegetables and short ribs:
Set he Instant Pot to a "sauté" setting and let it preheat. Add oil and sauté the vegetables for a few minutes. Don't stir too much, let them get a golden sear for more flavor.
Add garlic and sauté until fragrant. Take vegetables out of the pot and set aside.
Add a little more oil if needed and sear the ribs in batches of 3-4, depending on the size. Make sure to sear on all 4 sides. Take them out and set aside.
Deglaze and cook:
Pour in red whine into the pot while scraping the bottom of the pot. Let it simmer for a couple of minutes and add back the ribs.
Add vegetables back to the pot as well.
Whisk together beef stock, balsamic vinegar, tomato paste, herbs, and seasoning and pour it into the pot.
Add bay leaves and gently stir everything.
Close the lid on the Instant Pot and make sure that it's latched. Turn the steam valve to "seal." Cancel sauté setting if it's still on and set the pot to cook on "stew/meat" setting for 45 minutes. (If the your pressure cooker does not have the "stew" setting, set it to cook on high pressure for 45 minutes.)
When the time is up, let it do a natural release for 10-15 minutes and then carefully turn the valve to manually release the pressure.
Carefully remove the ribs so you can thicken the sauce.
Set the cooking setting to "sauté" again.
Mix cornstarch and cold water together and whisk the mixture into the sauce in the pot. Let it simmer for a few minutes and stir while it simmers and thickens. Turn off the heat when it's done.