Preheat the oven to 300°F (150°C).
Season the pork shoulder generously with salt and pepper.
Heat the vegetable oil in a large Dutch oven over medium-high heat. Sear the pork on all sides until browned, about 5-7 minutes.
Remove the pork and set aside. Add the sliced onion to the pot and sauté until soft, about 5 minutes.
Stir in the minced garlic, fresh thyme, and Dijon mustard, cooking for an additional 1-2 minutes until fragrant.
Pour in the apple cider and chicken broth, stirring well to combine and deglaze the bottom of the pot.
Return the pork shoulder to the pot, ensuring it is partially submerged in the liquid.
Cover the Dutch oven and place it in the preheated oven. Braise for 4-5 hours, or until tender.
Once done, remove the pot from the oven and let the pork rest for 15-20 minutes before shredding.
Serve the shredded pork with the reduced braising liquid drizzled over the top.