1. Preheat the oven to 300º. Place the flour, salt, pepper, and half of the rosemary on a large plate, and mix well. Rub the shanks in the flour, coating them on all sides.
2. In a large, flameproof casserole or saute pan with a cover, heat 1 tablespoon of the oil over medium-high heat. Add the shanks (in two batches if necessary); cook about 3 to 4 minutes on each side, or until nicely browned, adding more oil if needed. When all of the meat is browned, remove the casserole from the heat and transfer the meat to a plate.
If you don't have one pot big enough for cooking the whole recipe at once: Heat two large frying pans simultaneously, adding 1 tablespoon of oil to each. Add the shanks in equal batches and saute for 3 to 4 minutes on each side, or until nicely browned, adding more oil if needed.
3. Use a paper towel to blot all but about a teaspoon of oil from the casserole or frying pans. Add the garlic, onions, shallots, and remaining rosemary to the casserole and saute about 2 minutes over medium-high heat (if using two pans, divide these and the remaining ingredients evenly between each pan). Remove the onion mixture with a slotted spoon to the plate with the meat.
4. Raise the heat to high and add the red wine (or chicken broth), allowing it to come to a boil. Reduce heat to medium and let simmer about 8 minutes. Add the broth and the lamb and onion mixture, and bring to a boil. Remove from heat, cover, and place it in the oven. (If you are using two pans, carefully transfer the vegetables and shanks to two 14 x 8 1/2-inch casserole dishes, then add the liquid. Cover the dishes with lids or tightly wrap in aluminum foil to cook.)
5. Cook the lamb for about 2 1/2 hours, or until it is very tender (almost falling off the bone) and the sauce is infused with the flavors of the lamb and herbs. Taste for seasoning, adding salt and pepper if desired. Sprinkle with the parsley before serving piping hot.
Pre-party prep: Make the dish a day ahead and refrigerate. Reheat in a 250-degree oven for about an hour.
*Note: Whether using lamb or veal, check with your butcher about availability; you may need to place a special order.
How kids can help: Mix flour, salt, pepper, and half of the rosemary for the meat rub.