Beef shanks are cut from the leg of the cow and tend to be tougher than other cuts of meat because of the frequent use of the leg muscle. To keep the meat from drying out on the grill, use a combination of direct and indirect cooking methods. Start by searing the meat directly over high heat. Then transfer the beef into a large pot and slow cook the shanks in a braising liquid over low heat. Baste the meat often to retain moisture while grilling.
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Season the beef shanks with salt and pepper.
Melt butter in a large pot. Add the carrots, celery and onions to the pot and saute until soft. Remove the vegetables from the heat and set aside.
Prepare a braising liquid for the beef shanks. Boil beef broth and water in a large pot. Season the braising liquid with thyme, bay leaves and the sauteed vegetables.
Preheat the grill to medium-high. Spray a small amount of olive oil on the grill grates.
Place the beef shanks directly on the hottest part of the grill. Sear each side of the beef for approximately 1 minute. Transfer the meat to the large pot with the braising liquid.
Reduce the heat of the grill to low. Cover the braising pot and move onto the grill grates.
Simmer the beef shanks over low heat for 2 hours. Baste the meat with braising liquid often while grilling.
Use a meat thermometer to take the internal temperature of the beef shanks. Remove the meat from the braising liquid when the meat is tender and starts to fall off of the bone.
Allow the meat to rest for approximately 3 minutes before slicing. Drizzle some braising liquid on the sliced meat and serve.