Wash and pat dry the oxtail pieces. Season with salt and pepper.
Add olive oil to the Instant Pot and turn on saute mode. When hot, add the oxtail and brown on all sides, about 3-5 minutes total.
Remove oxtail from the pot. Add the onion, celery, and carrot. Saute for 2 minutes. Add the garlic and saute for 30 seconds. Turn off saute mode.
Pour in the beef stock and red wine and whisk to remove the browned bits from the bottom of the pot. Add the tomato paste, thyme, and rosemary. Stir well. Add back in the oxtail.
Lock the Instant Pot lid and set the vent to sealing. Pressure cook on high for 45 minutes. When finished, allow a natural release of pressure (about 15 minutes).
The oxtail to a serving bowl. Remove any excess fat or grease from the cooking liquid. If you wish to thicken the sauce, turn back on saute mode and cook until reduced to your liking.
Serve the oxtail with the sauce poured over.
Notes
Before pressure cooking, always take the time to sear the oxtail pieces using the "Sauté" function on your Instant Pot. This browning process, known as the Maillard reaction, enhances the flavor of the meat and adds depth to the final dish.
Due to its dense nature, oxtail can handle (and requires) a good amount of seasoning. Don't be shy with salt and spices. Additionally, consider marinating the oxtail in advance for extra flavor.
You'll need liquid for pressure cooking, and it's an opportunity to infuse more flavor. Beef broth, red wine, or even a dark stout beer can add delicious complexity to the dish.
After the cooking cycle, allow the Instant Pot to release pressure naturally. This lets the oxtail continue to cook and tenderize in the remaining heat and steam. It also allows the flavors to meld together even more.
Oxtail can be quite fatty. After cooking, consider chilling the dish in the fridge. The fat will rise to the top and solidify, making it easy to remove.
Oxtail dishes often taste better the next day, once the flavors have had time to meld together. If you have the time, consider making your oxtail a day in advance of when you plan to serve it.