Season the pork with the salt and pepper and heat the oil in a large skillet over medium-high heat.
Sear the pork until dark brown on two broad sides, 4 to 5 minutes per side, then transfer it to a 6-quart slow cooker.
Add the onion, mustard, cider, vinegar and thyme, turning the pork once to coat it.
Cover and cook on low until the pork pulls apart under a fork, 7 to 8 hours.
Nestle the apple wedges into the liquid for the final 45 minutes so they soften without disappearing.
Transfer the pork and apples to a platter and skim excess fat from the cooking liquid.
Whisk the cornstarch with the cold water, stir it into the cooker and cook on high until the gravy thickens, 8 to 10 minutes.
Pull the pork into large pieces and spoon the cider gravy over it.