Preheat the oven to 325°F
Season the pork with the salt and pepper.
Heat the oil in a large Dutch oven over medium-high heat. Once the oil is hot, add the pork and brown well on all sides, 3 to 4 minutes per side.
Remove the pork and add the onion wedges to the pot. Cook for a few minutes, letting them get a little color but being careful not to let them burn.
Return the pork to the pot, placing it on the bed of onions. Add the Lucky Dog and 1 cup water and bring to a simmer, then wedge the apple pieces under the meat among the onions. Toss in the thyme.
Cover and transfer to the oven. Cook for 3 hours, or until the meat is fork-tender, shreds easily, and is a deep brown color; the apples will have caramelized.