The night before cooking the pulled pork, mix all the dry rub ingredients together in a bowl.
Place the pork in a glass baking dish and coat all sides of the meat with the dry rub seasonings. Cover with plastic wrap and refrigerate for at least 12 hours.
The next morning, remove the pork from the refrigerator and allow to sit at room temperature for 30 minutes.
Heat a large cast iron skillet over medium high heat. Season with a bit of olive oil.
Place the pork onto the hot skillet and brown all sides.
Once the pork is browned, place it in the crockpot on low heat.
Mix applesauce with water and pour into the crockpot.
Cover and slow cook the pork for 6-8 hours.
Once the pork is tender and ready to be shredded, remove it from the crockpot, shred and discard the fatty pieces.
Return the shredded pork to the crockpot and stir to combine with the sauce inside.
Allow the juices to reabsorb into the pork for 30 minutes before serving.
Pulled pork can be stored in the refrigerator for up to 4 days. It can also be frozen for up to 3 months.