Preheat oven to 325°F.
Pat the pork dry with paper towels.
Season with salt and pepper evenly.
Heat oil in the Dutch oven.
Sear pork until golden on all sides.
Remove pork and set aside.
Add onions and garlic, sauté until soft.
Stir in apples and cook for 2 minutes.
Add cider, broth, mustard, and vinegar.
Scrape browned bits from the bottom.
Return pork to the pot.
Add thyme and bay leaf.
Cover with lid or foil.
Transfer to oven and braise 3 hours.
Remove lid for last 20 minutes.
Check tenderness; pork should shred easily.
Discard bay leaf and thyme sprigs.
Serve warm with your favorite sides.