+1 with Ed.
The old-school way is to sieve the braising liquid, then use the back of a spoon to press the essences of the old mirepoix into the stock. Reduce and/or use a thickening agent while the braised shanks are resting. Adjust the seasoning.
Prepare the braising stock in advance using roasted lamb bones and mirepoix. Strain and reserve.
Brown the lamb, add some tomato paste to the pot, and brown that too. Deglaze with wine, add the reserved stock to half way up the meat (as Chris rightly said) along with a generous helping of thick sliced onions, but no other veg. Bring to the boil, cover and put in a slow or medium oven.
After the lamb is finished and resting, rest the liquid so you can defat it. Add some wine or "cognac" to it, bring up the heat, reduce until it has some structure. You may enrich -- if desired -- with a little cream, creme fraiche, sour cream or rich yogurt. Add the cream near the end of the reduction, and the cultured dairy after reduction and off the heat. Don't forget to adjust the seasoning.
Sauce the lamb, including some of the onions. Pile the reminder on crostini, buttered toast, or other hot bread; and eat the bread along with the lamb as the primary starch. Side with mixed, roasted vegetables. Sprinkle the lamb generously with gremolata, and serve plenty more gremolata in small side dishes.
Another, different way:
Season the lamb with a beef rub, but heavy on the rosemary and garlic. Smoke lamb shanks low and slow. Serve with greens, and creamy smashed potatoes. Plate the potatoes separately, and smother the lamb and greens in a tangy, spicy, tomato based barbecue sauce. No gremolata, but you do need a smoker of some sort.
Edited by boar_d_laze - 10/9/11 at 7:27pm