Preheat and prep. Heat the oven to 300°F (150°C).
Pat the pork shoulder dry with paper towels. Mix salt, pepper, paprika, and oregano. Rub the seasoning all over the meat, getting into the crevices.
Sear for flavor. Heat the oil in a large Dutch oven over medium-high heat.
Sear the pork shoulder on all sides until deeply browned, about 3–4 minutes per side. Transfer the pork to a plate.
Build the base. In the same pot, add the onion, carrots, and celery with a pinch of salt. Cook 5–7 minutes, stirring and scraping up browned bits.
Add the garlic and tomato paste; cook 1–2 minutes until the paste darkens slightly.
Deglaze. Pour in the wine. Simmer 2–3 minutes to reduce by half, scraping the bottom of the pot. Add the stock, bay leaves, and thyme.
Stir to combine.
Braise low and slow. Return the pork (and any juices) to the pot, nestling it into the liquid. The liquid should come about halfway up the meat; add more stock if needed. Cover with the lid and transfer to the oven.
Cook until tender. Braise for 3–4 hours, turning the pork once halfway through.
It’s done when a fork slides in easily and the meat starts to separate. For boneless, start checking at 3 hours; bone-in may need closer to 4.
Adjust and finish. Transfer the pork to a platter and tent loosely with foil. Skim excess fat from the surface of the liquid.
Simmer the braising liquid on the stove over medium heat for 5–10 minutes to thicken slightly. Stir in the apple cider vinegar and adjust salt and pepper to taste.
Serve. Shred or slice the pork. Spoon the reduced sauce and vegetables over the top.
Serve with mashed potatoes, creamy polenta, rice, or crusty bread to catch the juices.