Preheat your oven to 300°F (150°C).

In a large Dutch oven or heavy pot, heat the olive oil over medium-high heat. Add the pork shoulder chunks and sear 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. Add 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. Stir in the chicken broth, apple cider vinegar, brown sugar, Dijon mustard, thyme, rosemary, salt, and black pepper.

Return the seared pork shoulder to the pot and add the sliced apples. Bring the mixture to a simmer.

Cover the pot with a lid and transfer it to the preheated oven. Braise for 3 to 4 hours, or until the pork is tender and easily pulls apart with a fork.

Once done, remove the pot from the oven and let it rest for 10 minutes before serving. Garnish with chopped parsley.