Preheat an oven to 325. Pat the pork pieces dry with a paper towel and season with kosher salt and pepper.
5 Pounds Pork Butt, Kosher Salt, Black Pepper
Heat the oil in a large dutch oven over medium-high heat. Once the oil is hot, put the pork in, in a single layer. Sear for 4-5 minutes per side until the pork is deeply browned. Repeat on each side.
2 Tablespoons Canola Oil
While the pork is searing, whisk together the apple cider, chicken stock, vinegar, brown sugar, mustard and a pinch of salt and pepper and set aside.
2 1/2 Cups Apple Cider, 1 1/2 Cups Chicken Stock, 2 Tablespoons Apple Cider Vinegar, 2 Tablespoons Dark Brown Sugar, 2 teaspoons Dijon Mustard, Kosher Salt, Black Pepper
Once the pork is browned all over, pour in the braising liquid. Arrange the herbs and onions around the pork in a pan. Place the garlic head in the pot with the pork, and the butter on top of the pork. Cover and place in the oven.
1 Head Garlic, 3 Sprigs Rosemary, 4 Sprigs Thyme, 1 Red Onion, 1 Tablespoon Butter
Braise for 3 hours, start checking at 2 1/2 hours for boneless), flip the pork halfway through. Once the pork is just shy of fork tender, remove the pork from the oven and arrange the apples around the pork. Cover and return to the oven for 50 minutes to 1 hour.
2 Granny Smith Apples
The pork should be very tender at this point. Remove the pork and let it rest 20 minutes before serving.
Squeeze the garlic cloves out, smashing them as you do and add back into the broth. Serve with the apples, onions and sauce over the pork.