Pat the pork dry with a paper towel. Evenly salt all sides of the pork.
Heat the oil in a large (oven proof) dutch oven set over high heat. Brown the pork shoulder roast until brown on all sides, about 4 minutes each side. Then transfer to a plate.
Add shallots and fennel to the oil and reduce heat to medium. Cook for 5 minutes. (deglaze the pan with 1/4 cup chicken stock if it is browning to quickly) Add in garlic and cook for 1 more minute. Scoop out as many of the apples, fennel, and shallots as you can onto a plate and set aside.
Add the pepper, cayenne, fennel seeds, apple cider, apple cider vinegar, chicken stock and stir to combine. Add just the pork back to the pot and bring to a boil over high heat
Cover the pot with a tight fitting lid. Place the meat in the oven for 2 ½ hours.
About 30 minutes before the meat is done, add the apples, fennel, and shallots to the pot, nestling them down into the liquid. Place the lid back on and continue cooking until done.