Preheat the oven to 350°F with a rack in the center position.

Pat the pork completely dry with paper towels and season all over with the salt.

Heat the olive oil in a large Dutch oven over high heat. Once the oil is glistening, sear the pork shoulder on all sides until well browned, about 4 minutes per side. Transfer to a plate.

Reduce the heat to medium. Add the shallot and fennel to the same Dutch oven and cook, stirring occasionally, until softened and lightly caramelized, about 5 minutes. If the veggies begin to brown too quickly, add ¼ cup of the chicken stock to deglaze. Add the garlic and cook, stirring, until fragrant, about 1 more minute. Transfer the vegetables to a separate plate.

Add the black pepper, cayenne, fennel seeds (if using), apple cider, apple cider vinegar, and chicken stock to the Dutch oven. Increase the heat to high and bring to a boil, scraping up any browned bits from the bottom of the pan.

Return the pork to the Dutch oven. The liquid should come about half way up the sides of the meat. Cover with a tight-fitting lid and transfer to the oven. Braise for 2 hours.

Remove the Dutch oven from the oven and add the apples and cooked vegetables. Cover and return to the oven for another 30 minutes, or until the pork is tender and easily shreds.

Let the pork rest for 10 minutes before slicing or shredding. Serve with the apples and vegetables, spoon the braising liquid over the top. Garnish with reserved fennel fronds, if desired.