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1
Combine the 8 cups hot water, the salt, and sugar in a large saucepan. Bring to a boil over high heat and boil until the salt and sugar dissolve. Remove from the heat and let cool. Chop the garlic and rosemary in a food processor or by hand.
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2
Pour the 8 cups cold water into a small cooler, a tub, a clean heavy-duty trash bag, or another container just big enough to hold whatever it is you are brining. Pour in the cooled sugar/saltwater, the ice, and the chopped garlic and rosemary. The ice will melt as the brine sits.
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3
Put a large, heavy-duty trash bag in a large bowl or tub (something large enough to hold the lamb) and carefully pour in the brine. Add the lamb and push it down until it is completely submerged. Press the air out of the bag, tie it closed, and put the container and bag in the refrigerator for 3 days.
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4
Preheat the oven to 300u00b0F. Make a layer of the vegetable chunks on the bottom of a roasting pan that is large enough to fit the lamb. Pull the lamb from the brine and discard the brine. Place the lamb on the vegetables and roast until fork-tender, 4 to 5 hours. Let cool to room temperature.
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5
Remove the cooled lamb to a cutting board and remove the bones. The lamb should be tender enough to pull the bones right out of the meat. Try to keep the sections of meat as whole as possible.
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6
Slice the lamb sections into 1-inch-thick pieces. Heat the oil in a large skillet over high heat. Brown the lamb pieces in the hot oil until crispy, 3 to 4 minutes per side, turning occasionally. Serve the seared lamb pieces on a platter sprinkled with salt, pepper, and fresh rosemary leaves.
