In small bowl, combine brown sugar, paprika, salt, mustard powder, cumin, chili powder and pepper. Stir to combine.
Rinse and pat dry pork roast. Trim any excess fat. Coat roast with dry rub.
Heat heavy bottom dutch oven or skillet on high. Add vegetable oil. When oil is hot, add roast and brown on all sides, about 2 minutes each side.
Add browned roast to slow cooker. Add apple cider, cider vinegar, and chicken broth. Cook on low 8 hours.
When done, transfer roast to plate to cool. When cool enough to handle, shred meat, discarding any fat and bones.
Strain liquid from slow cooker. Cook over medium heat until reduced to about 1 cup, about 10-20 minutes. Return shredded meat and reduced liquid to slow cooker, stir, and heat until warm. Season with additional salt or apple cider vinegar, if desired. Serve with BBQ sauce, cider slaw, and homemade buns.