Combine the apple cider, garlic, and rosemary in a large zip-top bag or dish. Add the pork loin, seal, and refrigerate for at least 12 hours or up to 3 days.
Remove the pork from the marinade and pat completely dry with paper towels. Discard the marinade. Season liberally on all sides with salt and pepper.
Preheat the oven to 400°F.
Heat the olive oil in a 10- to 12-inch cast iron skillet over medium-high heat until shimmering. Sear the pork on all four sides, about 2 to 3 minutes per side, until golden brown and the meat releases easily from the pan.
Transfer the skillet to the oven and roast uncovered for 45 to 60 minutes, or until an instant-read thermometer inserted into the thickest part reads 145°F. Plan on roughly 15 minutes per pound and start checking at 40 minutes.
Transfer the skillet to the oven and roast uncovered for 45 to 60 minutes, or until an instant-read thermometer inserted into the thickest part reads 145°F. Plan on roughly 15 minutes per pound and start checking at 40 minutes.
Tent loosely with foil and rest 15 to 20 minutes before slicing.
While the pork rests, warm the barbecue sauce in a small saucepan over low heat.
Slice thinly against the grain, drizzle with the warm sauce, and garnish with fresh rosemary.