To make the lamb shanks: Pat lamb shanks dry and season with salt and pepper. In an 8 quart heavy flameproof casserole heat oil over moderately high heat until hot but not smoking and brown lamb shanks well in batches, transferring to a plate as browned. To casserole add onion, carrot, celery, and garlic and saute until onion is softened. Add wine and simmer mixture, stirring occasionally, until liquid is reduced to about 3 cups. Return lamb shanks to casserole and stir in broth, tomato paste, and thyme. Bring liquid to a boil and simmer, covered, stirring and turning lamb shanks occasionally, 1 1/2 hours. Simmer mixture, uncovered, stirring occasionally, 1 hour more, or until lamb shanks are tender.
To make the Gremolata while lamb is cooking: In a small bowl stir together gremolata ingredients.
To make the Beans while lamb is cooking: In a saucepan heat oil over moderately high heat until hot but not smoking and cook onions, carrots, celery, and garlic, stirring, 2 or 3 minutes, or until softened. Add beans, 2 cups broth, butter, and bay leaf and cook over moderate heat, stirring occasionally and adding enough remaining broth to keep beans moist and to reach a creamy consistency, about 30 minutes. Discard bay leaf and add half of gremolata and salt and pepper, to taste.
Transfer lamb shanks to a plate and keep warm, covered with foil. Strain braising liquid through a sieve into a saucepan, discarding solids. Boil sauce, stirring occasionally, until thickened slightly. Pour sauce into a bowl and season with salt and freshly ground black pepper. Stir in the butter and tarragon.
Sprinkle lamb shanks with remaining gremolata and serve with beans and sauce.
Recipe courtesy of Gourmet Magazine