Preheat oven to 350 °F
Cut the pork shoulder into large chunks, then chop the Celery, Carrot, Onion, and Garlic. Put your Dutch oven on a large burner over medium high heat and add Olive Oil. Let the Oil heat up.
Working in batches, braise all sides of the pork pieces until they have a golden brown crust. Remove the pork and set aside.
Reduce the heat to medium and cook the Celery, Carrot, and Onion for a few minutes or until softened. Add the Garlic and cook another minute. Mix in the Salt, Pepper, and Tomato Paste. Cook for one to two minutes.
Add the Apple Cider Vinegar and use wooden spoon or spatula to deglaze the bottom of the Dutch Oven (Break up the brown bits cooked to the bottom of your pan). This step is important for adding flavor back into the dish.
Return the Pork to the Dutch Oven and add Beef Broth until all but the very top of the pork is covered. Add the Bay Leaves and Parsley (Yes, the whole bunch), then place the lid on the Dutch Oven.
Place the Dutch oven in the preheated oven and cook for three hours or until fork tender. Let the dish rest 5 minutes then discard the Bay Leaves and Parsley. Place pork on a plate and spoon a small amount of liquid from the bottom of the Dutch Oven over the meat before serving hot.