Pat the pork shoulder dry with paper towels.
Rub the pork with olive oil, smoked paprika, garlic powder, onion powder, salt, and black pepper.
Place the pork into a slow cooker and pour in the chicken broth.
Cover and cook on LOW for 8 to 10 hours or HIGH for 5 to 6 hours until the pork is fork-tender.
Remove the pork from the slow cooker and shred it using two forks.
Discard excess fat and return the shredded pork to the slow cooker.
Mix in the barbecue sauce and stir until evenly coated.
In a medium bowl, combine the coleslaw mix, mayonnaise, apple cider vinegar, honey, salt, and pepper.
Stir until well combined and refrigerate until ready to serve.
Slice the slider buns in half and lightly brush the tops with melted butter.
Toast the buns lightly if desired.
Pile the pulled pork onto the bottom halves of the buns.
Top with coleslaw and place the bun tops over the filling.
Serve immediately while warm.