Trim excess fat from pork and cut into 4 pieces.
Combine brown sugar, chili powder, salt, garlic powder, onion powder, cumin and cinnamon in a small bowl. Rub spice mixture all over the pork.
Turn the Instant Pot to the SAUTE setting. Add olive oil and allow to get hot. Working in batches (2 pieces of pork per batch) add pork to the Instant Pot and allow to brown on all sides (about 5 minutes per batch). Remove pork and set aside.
Turn Instant Pot off (CANCEL). Add ½ cup water and use a wooden spoon to deglaze (scrape the brown bits from) the bottom of the pot. Whisk in 1 cup chicken broth and 1 cup BBQ sauce. Add pork pieces.
Lock lid, set vent to SEALING. Select MANUAL/PRESSURE COOK and set to 45 minutes on HIGH PRESSURE. When cooking cycle is complete, allow Instant Pot to NATURAL RELEASE for 10 minutes and then do a QUICK RELEASE to release any remaining pressure.
Transfer pork to a large bowl (retaining cooking liquids). When pork is cool enough to work with, use the tines of two forks to shred pork.
Allow cooking liquid to stand for at least 10 minutes. Use a spoon or ladle to remove any fat from the top of the liquid. Reserve 2 cups of liquid and discard any additional liquid (or use for another purpose) from the Instant Pot. Add shredded pork and remaining 1 cup of BBQ sauce back to the Instant Pot. Add as much of the reserved cooking liquid as necessary to obtain desired consistency (you may not need the full 2 cups).
Serve in hamburger buns with extra BBQ sauce and coleslaw. Or, top baked potatoes and garnish with shredded cheddar cheese and sliced green onions