Combine apple juice, brown sugar, salt, peppercorns, garlic, rosemary and cloves in a saucepan. Bring to a simmer over medium heat and cook, whisking constantly, until salt has dissolved. Stir in ice to cool mixture. Transfer mixture to a container with lid; add pork chops, cover and refrigerate 1–2 hours.
Adjust oven rack to lower-middle position and heat oven to 450ºF (232ºC).
Heat a large cast-iron skillet over medium-high for about 2 minutes. Meanwhile, remove pork chops from brine and pat dry (thoroughly) with paper towels.
Add oil to skillet and swirl to coat. Once oil is shimmering, place chops in skillet and cook, without moving, for 2 minutes. Flip chops and cook on second side 2 minutes.
Flip chops once more then transfer to oven; roast chops until an instant-read thermometer inserted in center of each chop, but not touching bone, registers between 130–135ºF, about 8 minutes, turning chops over once halfway through cooking time.
Transfer chops to a clean sheet pan or cutting board; tent loosely with foil and let rest 5–10 minutes. Internal temperature should increase to 140ºF-145ºF.
Brush chops with barbeque sauce then slice and serve with additional barbeque sauce.