Apple cider vinegar cooks down with onions until caramelized to flavor the lamb with a sour-sweet flavor enhanced by aromatic rosemary. If the lamb you buy is boneless, aim for around 3 pounds in weight. If it’s bone-in, aim for around 4 pounds. This preparation also works well with the same cut of beef or pork.
Heat the oven to 350 degrees. Keep a heatproof bowl nearby. Season the lamb liberally with salt and pepper.
Heat 1 tablespoon olive oil in a large Dutch oven or heavy-bottomed pot over medium heat until it begins to shimmer. Add the lamb and cook, turning every 6 to 8 minutes or so, until the meat is evenly golden brown all over, about 20 minutes total. Transfer the lamb to a plate, and if there is more than 1 tablespoon fat in the pot, pour off the excess into the heatproof bowl.
Return the pot to medium heat and add the remaining 1 tablespoon olive oil. Add the onions, season with salt, and cook, stirring occasionally and scraping the bottom of the pot to keep the browned bits from burning, until uniformly soft and translucent, 16 to 18 minutes. The onions will be browned, but that color will be from the browned bits on the bottom mixing with their moisture, not from caramelization. Add the wine and cook, stirring, until evaporated, about 3 minutes. Stir in the garlic cloves and rosemary and cook for about 1 minute more.
Pour in the vinegar and broth and stir, scraping the bottom of the pot to pick up the browned bits. Return the lamb to the pot and bring the liquid to a simmer. Cover the pot, and place it in the oven. Cook for 3 hours; the meat should easily fall apart when prodded with a spoon, and the onions will have reduced to a sludgy sauce.
Transfer the lamb to a serving platter; it will be very tender and may fall apart, so be careful when lifting it. Using tongs, twist and break apart the meat into large chunks and remove and discard the interior bone. Spoon the onions and garlic around the meat, sprinkle everything with a hefty pinch of flaky salt and serve.
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