Mix together brown sugar, paprika, garlic powder, onion powder, salt, and pepper in a small bowl to create a dry rub.
Pat the pork chunks dry with paper towels and rub the spice mixture all over the meat, coating all sides.
Pour chicken broth into the Instant Pot and place the seasoned pork pieces in the pot.
Close the lid, set the valve to sealing, and cook on high pressure for 60 minutes.
Allow natural pressure release for 15 minutes, then carefully quick release any remaining pressure.
Remove pork from the pot and shred with two forks. Discard most of the cooking liquid, leaving about ΒΌ cup.
Return shredded pork to the pot, stir in BBQ sauce, and let sit on the warm setting for 5 minutes to soak up the sauce. Serve on buns with coleslaw if desired.