Rub the pork with the spice mix, covering all the surfaces well.
Heat a large skillet over medium-high heat. Add the oil and heat until hot but not smoking. Swirl to coat the pan. Add the pork and brown on all sides, a few minutes per side. Watch closely so the spice coating doesn’t burn.
Transfer the pork to a slow cooker, then pour the BBQ sauce and chicken broth around the sides. Cover and cook until the meat is very tender and can be pulled apart with a fork, on high heat for 3 to 4 hours or on low heat for 6 to 8 hours.
Finish the pork: Remove the pork from the cooker and transfer to a cutting board. Spoon the oil off the top of the sauce. Shred the pork with two forks, removing any big chunks of fat, then return the meat to the sauce and stir together gently, adding white vinegar and salt to taste. Keep warm.
Make the slaw: Whisk together the buttermilk, olive oil, cider vinegar, 1/4 teaspoon salt, and 1/8 teaspoon pepper in a large bowl. Add the cabbage, carrots, apple, green onions, and cilantro, if using, and toss together. Season with more salt and pepper to taste.
Make the sliders: Scoop some of the pork into each bun and either top with some of the slaw or serve the slaw on the side. Serve immediately with the hot sauce, if using.