Season pork with salt and pepper. Heat oil in a large skillet over medium-high heat.
Sear two broad sides until dark brown, 4 to 5 minutes per side. Transfer to a 6-quart slow cooker.
Add onion, mustard, cider, vinegar, and thyme; turn pork once to coat.
Cover; cook on low for 7 to 8 hours until pork pulls apart with a fork.
Nestle apple wedges in the liquid for the final 45 minutes, until softened but intact.
Transfer pork and apples to a platter; skim excess fat from the liquid.
Whisk cornstarch with cold water; stir into the cooker. Cook on high for 8 to 10 minutes until gravy thickens.
Pull pork into large pieces; spoon over cider gravy.