Step 1: Prepare the Pork
1. Preheat Oven: Preheat your oven to 300°F (150°C).
2. Sear the Pork: In a large Dutch oven or heavy pot, heat the olive oil over medium-high heat. Season the pork shoulder with salt and pepper. Sear the pork on all sides until browned, about 3-4 minutes per side. Remove the pork from the pot and set aside.

Step 2: Sauté Aromatics
1. Cook Onions and Garlic: In the same pot, add the chopped onion and sauté until softened, about 5 minutes. Add the minced garlic and cook for an additional minute until fragrant.

Step 3: Add Liquids and Seasoning
1. Combine Ingredients: Pour in the apple cider, chicken broth, apple cider vinegar, brown sugar, Dijon mustard, cinnamon, and dried thyme. Stir to combine.
2. Return Pork: Place the seared pork shoulder back into the pot, nestling it into the liquid. Add the sliced apples on top.

Step 4: Braise the Pork
1. Cover and Cook: Cover the pot with a lid and transfer it to the preheated oven. Braise for 3-4 hours, or until the pork is fork-tender and easily shreds.

Step 5: Shred and Serve
1. Shred the Pork: Remove the pot from the oven. Carefully take out the pork shoulder and let it rest for a few minutes. Shred the pork using two forks.
2. Serve: Return the shredded pork to the pot and stir to combine with the sauce and apples. Serve warm, garnished with fresh thyme or parsley if desired.