Preheat your oven to 300°F (150°C).
In a large Dutch oven, heat the olive oil over medium-high heat. Add the pork shoulder chunks and sear them on all sides until browned, about 5-7 minutes. Remove the pork and set aside.
In the same pot, add the diced onion and cook until softened, about 5 minutes. Stir in the minced garlic and cook for an additional minute until fragrant.
Pour in the apple cider, scraping up any browned bits from the bottom of the pot. Add the chicken broth, apple cider vinegar, thyme, salt, and pepper. Stir to combine.
Return the pork shoulder to the pot and add the sliced apples on top. Bring the mixture to a simmer.
Cover the pot with a lid and transfer it to the preheated oven. Braise for 3-4 hours, or until the pork is tender and easily shredded with a fork.
Once cooked, remove the pot from the oven and let it sit for 10 minutes before serving. Garnish with fresh parsley.