Mix all of the spice rub ingredients in a small bowl.
Cut up pork shoulder into 4-5 large, equally-sized pieces and rub all sides with spice rub blend.
Turn Instant Pot on to saute mode and add oil. Once the oil is heated and shimmering, add in pork and brown all sides, about 1-2 minutes on each side. Don’t crowd the pot - this will steam the meat instead of browning. Brown the pork in multiple batches if needed.
Remove pork from the Instant Pot and use half of the broth to deglaze the pan, scraping up any browned bits with a wooden utensil. Turn off saute mode.
Stir in remaining broth, apple cider vinegar, bbq sauce, Worcestershire sauce, and liquid smoke.
Add the pork back into the Instant Pot, replace the lid, and set the steam vent to closed. Pressure cook on manual mode for 45 minutes at high pressure, then natural release for 20 minutes. After the 20 minutes is up, open the vent to release any excess pressure quickly.
Remove the pork and place it into a large bowl or serving platter. Shred with two forks and serve with a side of bbq sauce.