Sauté the garlic and rosemary in olive oil (or lard) in a heavy casserole until the garlic has been ever so lightly browned and fragrant. Remove both the garlic and the rosemary from the pot.
Add the lamb shanks to the seasoned fat and brown them well on all sides. Season them generously with salt and pepper, turning all the while. Add a splash of white wine to the pot, turning the lamb shanks around once again to coat them well.
Then cover the pot tightly and lower the heat. Let the lamb shanks simmer, covered, until very tender, about 2-1/2 hours or so. Moisten from time time, as needed, with a bit more wine or water.
About 20 minutes before the lamb is done, mash together the garlic and anchovy finely, then add a bit of the vinegar, enough to form a loose paste. Add this mixture to the lamb and mix well. Then finish simmering the lamb.
Serve hot. As part of a traditional Italian meal, this dish would a secondo. For a one-dish meal (but not in the usual Roman style but very nice all the same) accompany with some hot polenta.