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Peel and quarter the cloves from 2 heads garlic. Separate but do not peel the cloves from 3 heads garlic. Peel and cut in half the remaining 4 cloves.
Strain the beans from the soaking water, put into a large pot and cover with fresh water. Add the bacon, carrot, onion, the 4 cloves of garlic that have been cut in half and the fine sea salt. Bring the beans up to a boil over high heat, and then reduce heat to low. Cook the beans until they are tender, 45 minutes to 1 hour. More water may be added during the cooking process to keep the beans covered. Once cooked, remove from heat.
Place the leg of lamb on a large cutting board. Make small incisions in the meat in even intervals all over the leg. Stuff the incisions with the quartered garlic cloves and rosemary. Season the leg all over with the sel d'Antibes (or use salt and pepper). Place the leg, presentation-side up, in a large roasting pan. Arrange the unpeeled garlic cloves around the leg of lamb. Pour 2 cups water in the pan, put the lamb in the oven and cook until a meat thermometer reaches 145 to 165 degrees F., depending on how well you want it cooked, about 1 1/2 hours.
Once the lamb has reached desired doneness, remove from the oven and allow it to rest for 15 minutes. Once rested, move the lamb to a large cutting board. Slice the lamb into thin slices and arrange nicely on a large serving platter. Spoon the pan drippings over the sliced lamb to keep moist and garnish the platter with the roasted cloves of garlic from the bottom of the pan. Remove the carrot, onion and bacon from the beans, reheat them if necessary, and pour the beans into a large serving bowl. Sprinkle the beans with the vinegar.
Serve together family style.