Place the chopped onions in the bottom of a slow cooker. Place the pork shoulder on top of the onions and add garlic, ground mustard, cayenne pepper, brown sugar, salt, pepper, apple cider vinegar, and Worcestershire sauce. Pour Dr. Pepper on top and cook on high for 4 – 5 hours (or low for 8 hours).
Very carefully, remove it from the slow cooker and place on a large cutting board. Shred the pork and remove excess fat using forks. Place the shredded pork back into the slow cooker and continue to cook for an additional hour. Drain the remaining juices and toss the meat mixture in the BBQ sauce, adding a little at a time until the desired consistency.