Combine the brown sugar, smoked paprika, garlic powder, onion powder, cumin, chili powder, kosher salt, black pepper, and cayenne (if using) in a small bowl. Stir until evenly blended with no clumps, then taste a small pinch and adjust salt or spice level before applying to the meat.
Pat the pork shoulder completely dry with paper towels, rub olive oil all over the surface, then press the entire dry rub generously onto every side. For best results, wrap and refrigerate overnight or for at least 2 hours to allow the flavors to penetrate deeply.
Heat a cast iron skillet over medium-high heat until very hot, then sear the pork shoulder on all sides for 2-3 minutes per side until a deep brown crust forms. Transfer the seared pork to the slow cooker insert.
Whisk together the apple cider vinegar, chicken broth, Worcestershire sauce, and liquid smoke (if using), then pour the mixture around the base of the pork in the slow cooker without pouring over the top. The liquid should reach about 1 inch (2.5 cm) up the sides of the meat.
Cover and cook on LOW for 8-10 hours, or on HIGH for 5-6 hours, until the pork reaches an internal temperature of 195-205°F (90-96°C) and shreds effortlessly. Alternatively, braise in a covered Dutch oven at 300°F (150°C) for 4-5 hours.
During the last hour of cooking, combine all BBQ sauce ingredients in a small saucepan and bring to a gentle simmer over medium heat. Reduce to low and simmer for 15-20 minutes, stirring occasionally, until slightly thickened; taste and adjust seasoning as needed.
Transfer the cooked pork to a large cutting board and rest for 10-15 minutes, reserving 1/2 cup (120 ml) of the cooking liquid. Using two forks or bear claw shredders, pull the pork into long thin strands, discarding any large pieces of fat or bone.
Transfer the shredded pork to a large bowl, pour the BBQ sauce over it, and toss to coat, starting with about 3/4 of the sauce. Add a few tablespoons of the reserved cooking liquid to keep the pork moist and flavorful.
Butter the cut sides of the brioche buns and toast in a skillet or under the broiler for 1-2 minutes until golden. Pile a generous portion of sauced pulled pork onto the bottom bun, top with coleslaw and pickled jalapeños or pickles if desired, and serve immediately.