Cider-Braised Pork Roast

Using sharp knife, trim fat cap on roast to 1/4 inch. Cut 1-inch crosshatch pattern, 1/16 inch deep, in fat cap. Place roast on large sheet of plastic wrap. Combine sugar and 1/4 cup salt in bowl and rub mixture over entire roast and into slits. Wrap roast tightly in double layer of plastic, place on plate, and refrigerate for 18 to 24 hours.

Adjust oven rack to middle position and heat oven to 275 degrees. Unwrap roast and pat dry with paper towels, brushing away any excess salt mixture from surface. Season roast with pepper.

Heat oil in Dutch oven over medium-high heat until just smoking. Sear roast until well browned on all sides, about 3 minutes per side. Turn roast fat side up. Scatter onion and garlic around roast and cook until fragrant and beginning to brown, about 2 minutes. Add 1 3/4 cups cider, thyme sprigs, bay leaves, and cinnamon stick and bring to simmer. Cover, transfer to oven, and braise until fork slips easily in and out of meat and meat registers 190 degrees, 2 1/4 to 2 3/4 hours.

Transfer roast to carving board, tent with aluminum foil, and let rest for 30 minutes. Strain braising liquid through fine-mesh strainer into fat separator; discard solids and let liquid settle for at least 5 minutes.

About 10 minutes before roast is done resting, wipe out pot with paper towels. Spoon 1 1/2 tablespoons of clear, separated fat from top of fat separator into now-empty pot and heat over medium-high heat until shimmering. Season apples with salt and pepper. Space apples evenly in pot, cut side down, and cook until well browned on both cut sides, about 3 minutes per side. Transfer to platter and tent with foil.

Wipe out pot with paper towels. Return 2 cups defatted braising liquid to now-empty pot and bring to boil over high heat. Whisk in apple butter until incorporated. Whisk cornstarch and remaining 1/4 cup cider together in bowl and add to pot. Return to boil and cook until thickened, about 1 minute. Off heat, add vinegar and season with salt and pepper to taste. Cover sauce and keep warm.

To carve roast, cut around inverted T-shaped bone until it can be pulled free from roast (use clean dish towel to grasp bone if necessary). Slice pork and transfer to serving platter with apples. Pour 1 cup sauce over pork and apples. Serve, passing remaining sauce at table.