Store leftovers in an airtight container in the refrigerator for 3-5 days.
Oven method: Preheat oven to 325 degrees F. Cut the pork into 4 pieces (this will allow it to cook faster and more evenly in the pot). Season the pork on all sides and place in pot. Add an additional cup of water/broth to the pot. Prepare and season the pork the same, but cut it into a few large chunks to fit evenly into a dutch oven pan or oven-safe pot. Bake for 3-3/12 hours, until tender.
Instant Pot: Prepare and season the pork the same, inside the instant pot. Add an additional cup of water or chicken broth to the pot. Cook on Manual/High pressure for 70 minutes. When timer beeps, allow the pot to naturally release pressure, about 15 minutes longer. Remove lid and shred the meat. Broil if desired.
Make ahead Instructions: Add everything to the pot, cover and refrigerate for 1-2 days before cooking (depending on the freshness of your ingredients).
Freezing Instructions: Allow the pork to cool completely, then store in a freezer safe container or bag for up to 4 months. Thaw in the refrigerator overnight. To rewarm, spread the meat on a baking sheet with a little of the juice and reheat at 400 degrees F until warm, about 10-15 minutes.