Combine brown sugar, paprika, smoked paprika, garlic powder, onion powder, salt, and black pepper in a small bowl until well mixed.
2 tablespoons brown sugar, 1 tablespoon paprika, 1 tablespoon smoked paprika, 1 tablespoon garlic powder, 1 tablespoon onion powder, 2 teaspoons salt, 1 teaspoon black pepper
Pat pork shoulder dry with paper towels. Coat all sides with yellow mustard, then rub the dry spice mixture over the entire surface. Let rest at room temperature for 30 minutes.
4.5 lbs pork shoulder, 2 tablespoons yellow mustard
Place sliced onion at the bottom of the slow cooker. Pour chicken broth and apple cider vinegar over the onions. Set the pork shoulder on top, fat side up.
1 cup chicken broth, 0.25 cup apple cider vinegar, 1 medium yellow onion, 4.5 lbs pork shoulder
Cover and cook on low for 8-10 hours or on high for 4-6 hours. Check internal temperature after 8 hours; it should reach 195°F–205°F for easy shredding.
4.5 lbs pork shoulder
Transfer pork to a cutting board and rest for 15 minutes. Use forks or meat claws to shred into bite-sized pieces, discarding large fat chunks.
4.5 lbs pork shoulder
Mix shredded pork with barbecue sauce just before serving to retain texture and moisture.
1 cup barbecue sauce, 4.5 lbs pork shoulder