Start by removing the excess layer of skin and fat from the ribs. Season generously with salt and freshly ground pepper on all sides.
On the Instant Pot press on SAUTE twice to choose the MEDIUM setting, and heat the oil. The screen will show the HOT message. Add the short ribs to sear, meaty side down. Work in batches.
When browning the meat is done, remove the meat onto a plate and set it aside. Add onions to the pot (and a little bit of oil if needed), and saute for 2 minutes. Add the garlic cloves and tomato paste, and cook for 1 more minute. Switch off the SAUTE setting.
Deglaze the pot with the red wine scrubbing any bits stuck to the bottom of the pot with a wooden spoon. Add the beef or chicken stock, and soy sauce.
Add the carrot and celery and give everything a quick stir.
Add the beef ribs back in and a bay leaf, and fresh or dry thyme.
Secure the lid and set the vent to SEALING. Select the PRESSURE COOK/MANUAL setting and set the cooking time for 50 minutes at high pressure (45 for smaller ribs). The Instant Pot will take around 10-15 minutes to come to pressure and start cooking. When the cooking program ends, allow the steam to release naturally for 15 minutes then do a quick release.
Carefully remove the lid, and remove the short ribs onto a plate.