The shoulders, shanks and neck have a fair amount of connective tissue on them which is exactly what you want to keep your slow braises moist and it gives the finished sauce that incredible stickiness on your lips.
Try something like this
Heat a little duck fat or vegetable oil in a vessel big enough to hold your cut of meat. Brown off the meat and then remove from the pan. Add onions, carrots and celery and cook until softened. Add the meat back to the vessel with any vegetables or flavourings you might like.
We love leek and mushroom. Half cover the meat with wine and stock and seal the vessel with a lid or tin foil.
Cook at 140 for 3 hours, turn then cook a further 3-4 hours at 160.
You want the meat to easily pull away from the bone. Serve with a buttery mash and some wilted greens. Leftovers make a great ragu for pasta.
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