In a small bowl mix together 1 cup of BBQ sauce, brown sugar, garlic powder, cider vinegar, 1 cup of the chicken broth, the mustard, Worcestershire sauce, liquid smoke, chili powder and onion. Adjust to taste as you see fit. Set aside.
Turn your Instant pot to the sauté setting. Add enough olive oil to coat the bottom thoroughly.
Once the oil is hot, add the pork pieces into the pot and sauté until nicely browned on all sides. If they don't all fit, divide the pieces and fry them in batches.
Remove and place the pork pieces on a plate. Turn off the Instant Pot.
To deglaze the bottom of the Instant pot, pour in the remaining 1/2 cup chicken broth and scrape the brown bits from the bottom of the pot.
Add the browned pork to the Instant Pot, then pour in the BBQ mixture. Stir to cover the meat.
Close the lid and set the pressure value to sealing.
Cook on meat/stew or manual high pressure for 60 minutes.
Once the timer is done and the 60 minutes is up, let the pressure release naturally for 15 minutes, then do a quick release according to the manufacturer's instructions. This is a great time to get your buns and coleslaw ready!
Remove the meat from the instant pot and place in a large bowl. Add in 1/2 cup of the cooking liquid. Shred the meat with two forks until nicely pulled apart. Stir in the remaining BBQ sauce TO TASTE. You may not need it, taste first! You can add in the cooking liquid as you see fit as well to taste at this point.
Serve with buns and coleslaw.
cut the roast into 6-8 pieces if you want it to be fall-apart perfection when the 60 minutes are done.
Add in the cooking liquid at the end to taste. There is a lot of rendered fat in it, some of which IS definitely needed in the final product, but you may not want it all. Taking the roast out first lets you control how much you want.