Cooking very tough meats, such as lamb shank, involves some compromises. You'll earn the richest mouthfeel and tenderest texture by slow-cooking them at very low temperatures, either dry or in a flavorful liquid. Yet, the most savory flavors come from high-temperature cooking methods such as grilling. The simple solution is to slow-cook your shanks first, either by braising or low-temperature barbecue, then grilling them rapidly at the finish.
Use the tip of a sharp knife to remove the silver-gray sheath of connective tissue, called silverskin, from any parts of the shank where it's visible. Remove any areas of visible fat.
Place the shanks in a casserole dish or slow-cooker, and surround them with onions, celery, carrots and other flavoring ingredients, as desired. Pour in enough broth to come halfway up the shanks, or use any combination of broth, water and red wine.
Cover the casserole or slow-cooker with a lid. Cook on high in your slow- cooker for three to four, or on low for six to eight hours. For oven-braising, place the casserole dish in a preheated oven at 325 degrees Fahrenheit for two to three hours. If you're braising in a casserole, turn the shanks every 30 to 45 minutes to ensure even cooking.
Simmer the shanks until they're tender enough to easily insert a fork and twist off a morsel of the meat. Drain the meat thoroughly, and let it rest for at least 20 minutes while the grill preheats. During this time, strain the cooking juices, skim off any fat and thicken it to use as a sauce with the shanks.
Preheat the grill to a medium-high temperature, roughly 400 F to 450 F. Transfer the shanks to the grill, searing and browning them on all sides. Brush them with the cooking juices, if you wish, so they'll cook on and create an extra-flavorful surface. Transfer the shanks to a tray or individual plates, and serve them with their sauce and your choice of side dishes.
Build a bed of coals in the kettle of your charcoal grill. Rake the coals to one side of the grill, leaving the other side free for your shanks. Cover the grill and adjust the vents until the temperature stabilizes at 225 to 250 F. For a gas grill, light the burners on only one side or -- for a 3- or 4-burner model -- light the sides and leave the middle off. Preheat the grill to the same temperature range.
Trim the lamb shanks while your grill is preheating. Remove any visible fat or silverskin, and rub the shanks with salt and pepper or other seasonings of your choice. For a deeper flavor, season the shanks a day ahead and refrigerate them overnight.
Position the shanks on the unheated portion of your grill, leaving room between them for the hot air to circulate. Add a few small pieces of hardwood to the coals, if you wish, to give the lamb a smokier flavor. Close the lid, and stabilize the temperature at 225 F to 250 F.
Slow-cook the shanks for 1 1/2 to 3 hours, until they reach your desired degree of doneness and tenderness. Usually, shanks must be well done for the tough connective tissues to melt and dissolve, but feel free to experiment with other degrees of doneness.
Remove the shanks from the grill temporarily once they're done. Open the vents on your charcoal grill, or turn up the heat on your gas grill, until it reaches a temperature between 400 F and 450 F. Return the shanks to the grill for five to six minutes, turning them frequently, until they're well browned. Serve them hot with your choice of side dishes.