MAKES 6 SERVINGS
1. Preheat the oven to 350 degrees F. Place the lamb shanks in a large mixing bowl and add 2 teaspoons of salt and 1 teaspoon of black pepper. Toss the shanks well to make sure every bit of the salt and pepper is absorbed into the lamb. Add the flour and toss the lamb to coat thoroughly.
2. Melt 8 tablespoons of the butter with the oil in a Dutch oven or large heavy skillet over medium-high heat. When the foaming has subsided, add the shanks. You may need to do this in batches to avoid crowding the pan. If you crowd the pan you will steam the meat instead of browning it.
3. Brown, and I mean really brown, the shanks in the butter and oil on all sides until they are crusty, about 15 to 20 minutes. Be patient and pay attention, as this is truly the most important part of this dish. Transfer the browned shanks to a 9 by 13-inch baking dish and let them cool slightly.
4. Reduce the heat to low and add the remaining 4 tablespoons butter. Do not let the butter burn. The Dutch oven will be very hot. When the foaming has subsided, add the onions and sauté them for approximately 2 minutes, until they are just slightly translucent, and then add the celery and carrots. Sauté for 10 to 12 minutes, until the vegetables are just barely soft.
5. Remove the cooked vegetables and all pan juices to the baking dish or Dutch oven with the browned shanks, and then pour in 1 ½ cups of the chicken stock, and 1 ½ cups of the red wine. Add the remaining ½ teaspoon of salt and ½ teaspoon black pepper and add the thyme. Top the dish with the 2 bay leaves spaced equally on top. Cover and bake it in the preheated oven for 3 hours.
6. After this first half of baking add the remaining 1 cup chicken stock, 1 cup red wine, and the canned tomatoes and their juice. Cover and return to the oven for another 3 hours. After 6 hours total cooking time, remove the shanks from the oven, keep covered, and let them rest for 25 minutes. Uncover them, discard bay leaves, and use tongs to transfer the shanks to a serving platter. Spoon the vegetables and sauce over them, then serve.
7. Note: these shanks are infinitely better if they are cooked at least 1 day ahead, preferably 2 or 3. Reheat them, covered, at 325 f temperature for 45 minutes to an hour before serving.