In a small bowl, combine the brown sugar, smoked paprika, garlic powder, onion powder, salt, and pepper. Rub the mixture all over the pork chunks.
Press Sauté on the Instant Pot and heat the canola oil. Brown the pork on all sides, about 3 minutes per side. Work in batches if needed to avoid crowding.
Pour in the broth and scrape up any browned bits from the bottom of the pot.
Lock the lid and set the valve to Sealing. Select Pressure Cook (Manual) on High for 60 minutes.
When cooking finishes, let the pressure release naturally for 15 minutes, then carefully move the valve to Venting to release any remaining pressure.
Transfer the pork to a bowl and shred it with two forks. Stir in the BBQ sauce until well coated.
Pile the pulled pork onto toasted buns, top with coleslaw if desired, and serve.