1. Cook the lamb: Heat oven to 300?. Rub lamb with oil and season generously with salt and pepper. Heat a 6-qt. Dutch oven over medium-high heat. Add lamb and cook, turning occasionally, until browned on all sides, about 12 minutes. Transfer lamb to a plate. Add wine and 2 cups water to the Dutch oven; scrape up browned bits from bottom of pot. Nestle garlic and herbs into a large oval casserole; place lamb on top of herbs; add pan juices from Dutch oven. Cover lamb with foil; transfer to oven and roast, basting frequently, for 3 1/2 hours. Uncover, flip lamb, and continue to cook, basting frequently, until lamb is very tender, 3?-3 1/2 more hours. Transfer to a rack and let cool for 20 minutes.

2. Meanwhile, prepare the beans: About 1 1/2 hours before the lamb is done, drain beans and transfer to a 4-qt. saucepan along with 6 cups water, 4 cloves garlic, and the herb bundle. Insert the cloves into the onion and add to the pot. Bring to a boil, reduce heat to low, cover, and simmer until beans are tender, about 1 hour. Remove pot from heat and season with salt and pepper. Discard herbs and strain beans, reserving cooking liquid. Transfer 2 cups beans, 1/4 cup cooking liquid, oil, cr?me fra?che, and remaining garlic clove to a blender and pur?e. Stir pur?ed bean mixture and about 1 cup of the cooking liquid back into pot and cover to keep warm until lamb is cooked. Serve the lamb sliced or torn into chunks, alongside the beans.