¾teaspoonherbes de Provence, or a mixture of dried basil, thyme, rosemary, and fennel seed
2 strips orange zest (removed with a vegetable peeler)
1cup canned reduced-sodium chicken broth, or more as needed
Heat the olive oil in a nonreactive heavy, flameproof casserole or Dutch oven over medium heat. Season the shanks with salt and pepper to taste. Add them to the casserole and brown well on all sides, turning several times, 15 to 20 minutes total. Transfer to a plate; if there is excess fat, pour off all but a thin film from the casserole.
Preheat the oven to 325°F., with a rack positioned in the lower third of the oven. Add the onion, carrots, and celery to the casserole. Cook, stirring now and then with a wooden spoon, until the onions begin to soften, about 8 minutes. Add the garlic and cook, stirring, until the garlic is lightly golden, about 2 minutes.
Add the Cognac and boil until nearly dry. Add the white wine and boil until nearly dry. Add the tomatoes, herbes de Provence, orange zest, and bay leaf. Cook, crushing the tomatoes with a wooden spoon, until they reduce to the consistency of a thick tomato sauce, about 10 minutes. Stir in the broth and bring to a boil.
Place the lamb shanks in the liquid, adding any juices from the plate. The mixture in the casserole should reach halfway to two-thirds of the way up the lamb shanks; add more broth or cold water, if needed. Cover the casserole with foil to guarantee a tight seal and then cover with the lid.
Place the casserole in the oven and lower the heat to 300°. Braise until the lamb is very tender when poked with a paring knife, 2 to 3 hours. As the lamb cooks, turn the shanks over occasionally. If the liquid should begin boiling, lower the oven heat to 250° or 275° to maintain a gentle simmer (boiling the meat will toughen it).
Remove the casserole from the oven. Carefully remove the foil without letting any condensed liquid fall from the foil back into the pan. Remove and discard the bay leaf (and the orange zest, if you can find it). If you have time, let the casserole cool to room temperature; cover and refrigerate overnight. The solidified fat will lift easily off the surface. Or, if you don’t have the time to refrigerate the pot overnight, gently transfer the lamb shanks with a large slotted spoon to a plate, letting the juices fall back into the casserole. Cover the lamb shanks with foil and keep warm while you finish the sauce.
With a large metal spoon or skimmer, spoon off and discard all possible fat from the surface of the liquid. Place the casserole on a stove-top burner over medium-high heat. Boil, uncovered, until the juices thicken slightly, about 8 minutes.
Meanwhile, in a small bowl, combine the gremolata ingredients; set aside.
Add the cooked beans to the thickened liquid in the casserole; lower the heat, cover the pan, and simmer gently to heat through and combine flavors, about 10 minutes. Stir in the parsley. Taste and correct the seasonings, adding salt and pepper, if needed.
Place the shanks on warm dinner plates, pouring any exuded juices from the shanks into the beans. Spoon some of the beans next to or around each shank; spoon the juices over and around the shanks. Sprinkle with the gremolata mixture and serve hot.