For the lamb shank braise: Preheat oven to 315 degrees F. Trim excess fat from shank, heat cast iron pan. Add 1 tablespoon oil, season shank assertively with salt and pepper, and slowly brown all sides over medium high heat. Remove from pan, discarding excess oil. Add onion. Cook for 5 minutes. Add carrots, celery, garlic and bay leaf. Cook until vegetables are caramelized and tender. Add wine and reduce. Add chicken stock and bring to a simmer. Place shank in deep pan or dish. Pour vegetables and broth over shanks. Bring back to a simmer over medium heat. Cover and braise for about 1 hour 45 minutes or until meat is tender. Remove to cool. Strain vegetables from braising liquid. Simmer liquid to skim all that rises to the top and reduce by half. Pull meat from bone and set aside both meat and braising liquid.
For the beans: Cover beans with stock and water. Add bay leaf and vegetables, bringing to a simmer. Season to taste, continuing to simmer until beans are tender, about 45 minutes. Add more water as necessary.
For the marinade: Trim away silver skin from loin. Rub with marinade ingredients.
For the basil puree: Place garlic and a pinch of salt in a mortar. Puree, then add basil. Puree again. Slowly add olive oil to combine.
For the lamb loin and sausage: Grill the loin to medium rare and rest the meat for 5 minutes. Grill the sausage for about 7 minutes, then slice.
Heat the cannellini beans in the lamb shank braising liquid. Add the braised meat and sausage to the mixture. Slice the lamb loin against the grain. Spoon the ragout onto a plate, then arrange slices of lamb loin over the top. Drizzle with the basil puree and garnish with fresh basil.