Preheat the oven to 140C/275F/Gas 1.
For the lamb shanks, first remove the majority of fat from the shanks. Make three deep incisions in each shank and insert in each half an anchovy wrapped around a sprig of rosemary and a slice of garlic. Season the meat with salt and freshly ground black pepper - you will not need too much salt as the anchovies are very salty.
Heat a little duck fat, butter or dripping in a casserole, add the shanks and brown all over. Remove and set aside.
To the casserole, add the carrots, celery, leek, onions, garlic cloves and herbs and cook over a high heat until the vegetables are browned.
Deglaze the casserole by adding the red wine, scraping the residue on the bottom of the pan and stirring well.
Add the stock or water to the casserole, place the shanks on top of the vegetables, cover and cook in the oven for two and a half hours.
When the lamb has finished cooking, remove the four shanks to a dish and keep warm. Pass the vegetables and cooking liquor through a mouli, or blend in a food processor, and set to one side.
For the sauce, heat the oil in a large pan over a medium to high heat. Add the bacon and fry until browned. Reduce the heat and add the carrot, celery, onion and garlic.
Cook for eight minutes until the vegetables have softened then add the thyme, rosemary, tomatoes and flageolet beans. Heat through.
Pass the blended lamb cooking liquor and vegetables through a strainer or fine sieve onto the bean mixture, stir together and pour over the lamb shanks.
Mix the gremolata ingredients together to make the gremolata.
Serve the lamb garnished with the gremolata and parmesan.