Cut the pork shoulder into evenly sized 2- to 3-inch chunks, trimming only large areas of excess fat. Combine the brown sugar, paprika, salt, garlic powder, onion powder, chili powder, black pepper, and optional cayenne, then rub the mixture thoroughly over every piece of pork.

Set the Instant Pot to Sauté and add the neutral oil. Brown the pork in batches for about 2 to 3 minutes per side, transferring each browned batch to a plate as you work.

Turn off the Sauté setting and pour the chicken broth and apple cider vinegar into the pot. Scrape the bottom thoroughly to release all browned bits, since this helps prevent a burn warning during pressure cooking.

Add the sliced onion if using, return the pork to the pot, and pour in about 1/2 cup of the barbecue sauce. Make sure the broth and vinegar provide the thin cooking liquid rather than placing a large amount of thick sauce directly on the bottom.

Secure the lid, set the valve to sealing, and cook on High Pressure for 55 to 60 minutes for 3-inch pieces. A 4-pound roast or larger pieces may require 65 to 75 minutes.

When the cooking cycle ends, allow a natural pressure release for 15 to 20 minutes before carefully releasing any remaining pressure. This gradual release helps the pork stay tender and juicy.

Transfer the cooked pork to a large bowl and shred it with two forks, removing any large pieces of fat as you go. Strain or skim the cooking liquid if desired, then toss the pork with the remaining barbecue sauce and enough cooking liquid to reach your preferred consistency.

Serve the pulled pork immediately on buns, in tacos, in quesadillas, or over rice. For crisp edges, spread the sauced pork on a baking sheet and broil it for 3 to 5 minutes.