Season the lamb shanks with salt and pepper and dust with the flour, shaking off any excess. In a large cast-iron casserole, heat the olive oil until shimmering. Working in batches, cook the lamb over moderately high heat, turning, until browned all over, about 12 minutes per batch. Transfer the browned lamb to a plate. Add the carrots, celery, onion, garlic, thyme and bay leaves to the casserole and cook over moderate heat, stirring occasionally, until browned in spots. Add the wine and bring to a boil, scraping up the browned bits from the bottom of the casserole. Add the chicken broth and bring to a simmer. Return the lamb shanks and any accumulated juices to the casserole. Cover and simmer over low heat until the lamb is very tender, about 1 1/2 hours.
Transfer the lamb shanks to a plate. Strain the sauce into a bowl, then pour the sauce back into the casserole, discarding the vegetables. Bring the sauce to a boil and cook over high heat until thickened and reduced to 3 cups, about 10 minutes. Season with salt and pepper. Add the lamb back to the sauce and cook over moderate heat until hot, about 3 minutes. Transfer the lamb to shallow bowls, ladle some of the sauce on top and serve.