Press the Sauté button on the Instant Pot, and add the oil. Add pickled pork and sauté 5 minutes or until browned. Remove pickled pork to a paper-towel lined plate and reserve.
Add onions, bell pepper, celery, garlic and tomato paste to Instant Pot, and sauté until vegetables are soft.
Add pickled pork back to the pot, along with blackeye peas, water or broth, and bay leaves. Stir well.
Turn Sauté mode off. Cover Instant Pot, twist to lock the lid, and turn the valve to sealing. Press the Beans/Chili button, or use the Manual mode and set to 30 Minutes.
When the timer beeps, allow the pressure to release naturally for 20 minutes. Then, turn the valve to venting.
Remove lid. If a creamier texture is desired, and use the back of a spoon or potato masher to mash peas to desired consistency. Adjust seasonings to taste.
Serve over hot cooked rice with cornbread or hot buttered French bread. Garnish with chopped green onions.