Season the lamb with salt and freshly ground white pepper. Melt the dripping or oil in a large, lidded roomy casserole dish until hot. Place the lamb breast into the casserole dish, turn down the heat and colour well on all sides, until golden-brown. Lift out the meat and remove all fat from the dish with a spoon.
Add half of the onions to make a bed of onions on which to rest the lamb and add the lamb back into to the dish. Tuck in the bay leaf and cover with the remaining onions.
Cut a circle of greaseproof paper slightly bigger than the diameter of the dish. Dampen it, lightly grease one side, and press it onto the onions (greased side down). Put on the lid cook in the oven for about three hours. After an hour, remove the dish to see whether the onion mixture has reduced and to check that the natural juices are running. Scrape down the side of the dish if the onions have stuck. Replace the paper and lid and place the dish into the oven again.
After about three hours of cooking (check after another hour), push a skewer into the lamb to see how tender it is; there should be little resistance. Lift out the meat, put it into a small roasting tin and cover with foil. Turn down the oven to 140C/275F/Gas 1, and return the meat to the oven while you finish the onions.
Remove the bay leaf from the onions and drain the onions, reserving the cooking juices. Put the onions back into the casserole. Remove any fat that has settled on the surface of the cooking juices. Pour the liquid back in with the onions, and simmer until the volume of liquid has reduced by half. Stir in the vinegar and anchovy essence.
Season the onions to taste with salt and freshly ground black pepper. Finally, stir in the parsley.
Remove the lamb from the oven (if any meaty juices have exuded from the resting lamb, add them to the onions), cut off the strings and thickly slice the meat. Arrange the slices onto a hot serving dish and pile the onions alongside.