Preparation

Make the brine

• Put 2 cups of the cider in a small saucepan over medium-high heat. Bring to a simmer, and whisk in the sugar, salt, and garlic, adjusting the heat to maintain a simmer. Once the sugar and salt dissolve, remove the pan from the heat, add the remaining 2 cups cider, and let cool to room temperature. Transfer the loin to a large bowl or zip-top bag, pour in the brine, cover with plastic wrap or seal the bag, and refrigerate for 8 hours or overnight.

Roast the pork

• Position a rack in the center of the oven, and heat the oven to 425°F. Remove the pork from the brine, and transfer to a large plate lined with paper towels. Discard the brine, and pat the loin dry. Using kitchen twine, tie the loin in three places at even intervals. Slip the 12 whole sage leaves between the twine and meat, and season with 1 tsp. pepper.
• In a large roasting pan, toss the apples, potatoes, and onion with 1-1/2 Tbs. of the oil and 1 tsp. salt. Roast until mostly tender, about 25 minutes.
• Meanwhile, set a large heavy-duty skillet over medium-high heat. Add the remaining 1-1/2 Tbs. oil, and heat until shimmering. Set the loin in the skillet fat side down. Sear, undisturbed, until the meat browns and easily releases from the pan when you lift an edge with tongs, 2 to 3 minutes. Reduce the heat to medium, and sear the remaining sides, about 1 minute per side, or 6 minutes total. Set the skillet aside.
• Put the pork on top of the apples, potatoes, and onion in the roasting pan. Reduce the oven temperature to 350°F. Roast until an instant-read thermometer inserted into the thickest part of the roast registers 145°F, about 80 minutes; start checking after about 60 minutes. Remove from the oven, and let rest for 15 minutes.
• While the pork is resting, make a pan sauce. Pour off and discard any fat from the skillet, and set the pan over medium-high heat. Add the butter, flour, and torn sage leaves. Cook, stirring to scrape up any brown bits on the bottom of the pan, until the flour is lightly browned, about 1-1/2 minutes. Add the cider, and bring to a boil, stirring constantly. Reduce to a simmer and cook, stirring until thickened, about 5 minutes. Season to taste with salt and pepper.
• Remove the twine from the roast, and thinly slice the pork. Serve with the apples, potatoes, onion, and a generous drizzle of the sauce.