Mix together the salt, pepper, chili powder, and smoked paprika. Rub the spice mixture generously all over the pork shoulder.
Optional: Heat olive oil in a large skillet over medium-high heat. Sear the pork on all sides until a dark brown crust forms, about 3-4 minutes per side.
Place sliced onion and smashed garlic in the bottom of the slow cooker (if using). Place the pork on top.
Pour the applesauce over the pork.
Cover and cook on LOW for 8-10 hours or HIGH for 4-5 hours, until the pork shreds easily with a fork and reaches at least 195°F internally.
Remove the pork from the slow cooker. Shred with two forks, discarding any large pieces of fat.
Toss shredded pork with BBQ sauce if desired, and add a few spoonfuls of the cooking liquid for extra moisture. Serve on buns.
Notes
Pork cut: Use pork shoulder or pork butt. Do not use pork loin, it's too lean for pulled pork.
Searing: Optional but adds a rich, brown crust and deeper flavor. Worth the extra 10 minutes.
Low vs. high: LOW always produces more tender results. Use HIGH only if you're short on time.
BBQ sauce: Completely optional. The applesauce provides enough flavor on its own.
Storage: Refrigerate with cooking liquid for 4-5 days. Freeze in portions for up to 3 months.
Oven method: Sear in a Dutch oven, add applesauce and 1 cup apple cider, cover, and braise at 325°F for 2.5-3 hours.