Caucasus-Style Braised Pork Shoulder

Mince garlic, then mash to a paste with 2 teaspoons kosher salt using a heavy knife. Grind coriander and fenugreek seeds and red-pepper flakes to a powder in grinder, then stir together with garlic and 2 tablespoons oil in a small bowl. Make 2-inch-deep slits all over meat with a small sharp knife and push some of paste into slits. Rub remaining paste all over meat. Put pork in a bowl and marinate, covered and chilled, at least 8 hours.
Bring meat to room temperature, about 1 hour.
Put oven rack in lower third of oven and preheat oven to 350°F.
Heat remaining 2 tablespoons oil in a wide 5- to 6-quart heavy pot over moderately high heat until hot but not smoking, then brown pork on all sides, turning with tongs and a large kitchen fork, about 8 minutes total. Transfer pork to a large plate and cook onion in fat remaining in pot, stirring occasionally and scraping up brown bits, until beginning to brown, 7 to 8 minutes. Return pork to pot and add water and remaining teaspoon kosher salt. Bring to a boil, then cover tightly with lid and transfer to oven. Braise, turning meat once, until very tender, about 3 hours. Cool pork in pan juices completely, uncovered, about 1 1/2 hours, then chill, covered, at least 8 hours.
Put oven rack in lower third of oven and preheat oven to 350°F.
Remove fat from surface of pan juices and reheat pork (with pan juices), covered, in oven 1 hour. Transfer pork to a platter using cleaned tongs and large fork. Stir cilantro, vinegar, and table salt and pepper to taste into pan juices and serve with pork.