Cut your pork shoulder into 6 roughly equal pieces. Add them to a baking sheet or large plate so you don't make a mess when applying the rub.
Combine the brown sugar, smoked paprika, garlic powder, and chili powder in a small bowl. This is your spice rub.
Using your hands, coat the pork pieces in the spice rub as evenly as possible.
Add the olive oil to your Instant Pot and press the sauté button. Once the oil is hot, sear your pork on all sides (about 5 minutes per batch). You'll want to do 2 batches. Once seared, set the pork aside.
Add the chicken broth, Worcestershire sauce, and liquid smoke to your Instant Pot. Use a wooden spoon to ensure that any brown bits that stuck on are released from the bottom of the pot. Add the pork back in.
Close the Instant Pot's lid, set the valve on "sealing", and cook on high pressure for 60 minutes. It will take 10-15 minutes for it to get up to pressure.
Once the countdown has finished, carefully do a manual pressure release. Take the pork out of the Instant Pot once it has depressurized. Add it to a large bowl and shred it with 2 forks.
There will be a fair amount of juices left in the Instant Pot. I like to ladle some onto the shredded pork to moisten it and add some extra flavor. You could always boil it down or reserve it for another use if you wish.
Season the pork with salt & pepper as needed. Serve as desired (my favorite way is on a bun with my favorite BBQ sauce and homemade coleslaw). Enjoy!