In a small bowl, mix together brown sugar, paprika, garlic powder, onion powder, salt, black pepper, and cumin to create a dry rub.
Rub the spice mixture all over the pork shoulder chunks, making sure to coat all sides generously.
Pour chicken broth and apple cider vinegar into the Instant Pot, then place the seasoned pork chunks into the pot.
Close the lid, set the valve to sealing, and cook on high pressure for 60 minutes.
Allow for a natural pressure release for 15 minutes, then carefully switch the valve to venting to release any remaining pressure.
Remove the pork from the pot and shred it with two forks, discarding any large pieces of fat.
Return the shredded pork to the pot, stir in barbecue sauce, and mix well with some of the cooking liquid to keep it moist.
Serve on hamburger buns with additional barbecue sauce and your favorite coleslaw.