In a small bowl, mix paprika, chili powder, salt, and pepper. Rub this mixture over the pork shoulder.
Put the sliced onion and minced garlic at the base of the slow cooker.
Place the seasoned pork on top of the onions and garlic.
In a medium bowl, mix barbecue sauce, chicken broth, apple cider vinegar, brown sugar, and Worcestershire sauce. Then, pour this blend over the pork.
Cover and cook on low for 9-11 hours, or until the pork is tender and easily pulls apart.
Remove the pork from the slow cooker and shred it using two forks.
Remove excess fat from the liquid in the slow cooker. Add the shredded pork back to the slow cooker and mix it with the sauce.
Serve the pulled pork on toasted hamburger buns.