Mix the brown sugar, smoked paprika, garlic powder, onion powder, salt, and pepper. Pat the pork dry and rub the mixture all over, pressing it into the surface.
Heat the oil in a large skillet over medium-high heat. Sear the pork on all sides until deeply browned, about 3 minutes per side. Don't skip this — it's where the flavor starts.
Scatter the sliced onion in the slow cooker and set the seared pork on top. Pour the chicken broth and vinegar around the sides, not over the top, so the crust stays intact.
Cover and cook on LOW for 8 hours, until the pork shreds easily when pressed with a fork. Avoid lifting the lid while it cooks.
Transfer the pork to a large bowl and shred with two forks, discarding any large pieces of fat. Skim the fat from the cooking liquid and reserve the juices.
Return the shredded pork to the slow cooker with 1 cup of the reserved juices and the BBQ sauce. Toss to coat and keep warm until serving.