Step 1: Sear the Pork : Pat pork shoulder dry and season generously with salt and pepper. Heat olive oil in a large Dutch oven or oven-safe pot over medium-high heat. Sear pork on all sides until browned (3–4 minutes per side). Remove and set aside.
Step 2: Prepare Aromatics u0026 Braising Liquid : In the same pot, sauté onions until translucent, about 5 minutes. Add garlic and cook for 1 minute until fragrant. Pour in apple cider, broth, apple cider vinegar, and brown sugar. Stir to combine. Add thyme, rosemary, bay leaf, and optional apple slices. Bring to a simmer.
Step 3: Braise the Pork : Return pork to the pot, nestling it into the liquid. Cover with a lid and simmer on the stove over low heat for 2.5–3 hours, or bake in a preheated 325°F (165°C) oven for the same duration. Occasionally spoon liquid over the pork to keep it moist. Pork is done when it easily shreds with a fork.
Step 4: Rest and Slice/Pull : Remove pork from pot and let rest for 10 minutes. Slice or pull pork into pieces. Skim fat from braising liquid if desired, then spoon sauce over pork.