Trim any excess fat (but not all) from the pork shoulder, then cut into 4 equal pieces.
In a small bowl whisk together the brown sugar and all the seasonings; rub the spice mixture all over the pork pieces, getting in the nooks and crannies.
(Optional searing) Heat 1 tbsp oil in a large Dutch oven over medium-high heat. Working in batches if necessary, sear the pork pieces for 2-3 minutes per side until browned. Transfer to a plate.
Pour the chicken broth and vinegar into the bottom of a large Dutch oven or heavy-bottomed pot; stir to combine. Add seasoned pork pieces to the pot.
Cover pot with lid, place in a 300°F preheated oven, and cook for 3 hours. Remove lid and cook for an additional 1-2 hours, or until pork is very tender and easily separates when pulled with a fork.
Remove from oven and let rest for 10-15 minutes. Transfer pork to a clean work surface and shred with two forks.
Drizzle a little of the pot juices over the meat to moisten, if necessary. Serve as desired.