Mix smoked paprika, garlic powder, onion powder, salt, and pepper. Rub this mixture all over the pork.
Place the pork into the crock pot. Pour in barbecue sauce, Dr Pepper, and chicken broth.
Cover and cook on low for 8 to 10 hours, or until the pork is fork-tender.
Shred the pork using two forks, then mix it back into the juices in the crock pot.
For the coleslaw, combine cabbage, carrots, mayonnaise, vinegar, honey, salt, and pepper in a bowl. Toss until everything is coated.
Serve the pulled pork on buns topped with homemade coleslaw.