Press the “Sauté” button on the Instant Pot®. Add 1 tablespoon olive oil and half the pork shoulder and season with one-half teaspoon garlic powder, plus salt and black pepper, to taste.
Sear until pork is browned on all sides, approximately 1-2 minutes per side, before transferring to a large, rimmed plate. Set aside.
Repeat Step #2 with another tablespoon of olive oil and the remaining pork and garlic powder. Season with additional salt and black pepper, as desired.
Once seared, transfer to the rimmed plate with the rest of the pork and set aside.
Add remaining olive oil, plus the red onion and shallot. Cook, stirring frequently, until soft, approximately 3-4 minutes.
Deglaze Instant Pot® by adding the chicken broth and gently scraping the bottom of the container with a plastic spatula to loosen any browned bits.
Pour in the apple cider vinegar and three-quarter cups of BBQ sauce. Return the seared pork and its juices to the unit and cover, locking the lid into place.
Set the pressure valve to “sealing” and select the “Manual” option on the highest setting. Adjust cook time to 50 minutes.
When cook time is complete, allow the pressure to release naturally for 10 minutes, and then do a quick release for any remaining pressure.
Carefully remove the lid and shred the pork with two forks. Allow the shredded pork to sit in the warm liquid for 5 minutes to soak up more flavor before serving if desired.
To serve, transfer the shredded pork with tongs to a large bowl and toss with the remaining BBQ sauce.
To serve, divide the shredded pork between the toasted slider buns and top with some of the cabbage slaw.