Preheat oven to 325 degrees F.
Score fat and any skin on pork in a crosshatch pattern. Make slits all over meat with a small sharp knife and insert a garlic sliver in each slit. Pat pork dry and season with salt and pepper.
Heat oil in a 4 to 5-quart ovenproof heavy pot over moderately high heat until hot but not smoking, then brown meat on all sides, turning occasionally with the aid of tongs and a carving fork, about 8 minutes. Transfer pork to a plate.
Add onions to pot and saute over moderately high heat, stirring occasionally, until softened and starting to turn golden, about 5 minutes. Add 3/4 teaspoon salt and saute, stirring occasionally, until onions are golden and caramelized, 8 to 10 minutes more.
Stir in cider and return pork to pot. Cover pot with a tight-fitting lid and braise pork in middle of oven until very tender, 3 1/2 hours.
Transfer pork to a serving dish with the aid of tongs and carving fork. Boil cooking juices with onions until mixture is reduced to about 2 cups, 2 to 3 minutes, then season with salt and pepper and serve with pork.
Note: Pork can be made 1 day ahead. Cool, uncovered, then chill, covered. Reheat in liquid, covered, at 325 degrees F, for 1 hour.
Recipe courtesy of Gourmet Magazine