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Heat oven to 160C/140C fan/gas 3 and sit a shelf as low as possible. Pierce the lamb all over with a small knife, then fill each slit with a garlic clove and half an anchovy fillet. Rub all over with the oil, then season.
Heat a flameproof casserole dish and sear the lamb all over until well browned. Take off the heat, remove the lamb from the dish and tip in the tomatoes, carrots, sage and rosemary. Sit the lamb on top and scatter over the thyme.
Cover the dish, slip it onto the bottom shelf of the oven and cook for 4-5 hrs until pull-apart tender. Carefully lift the lamb from the dish, discard the herbs and roughly squash the tomatoes into the juices. Sit the lamb back in the dish and serve in big shredded chunks with tzatziki, chickpea salad and flatbreads for mopping up the juices.