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Put the lamb on a chopping board, flesh-side up, and season all over generously. Scatter over the garlic, chopped rosemary and lemon zest, then roll up tightly lengthways and secure with kitchen string.
Heat the oven to 170C/150C fan/gas 3. Heat the oil in a large flameproof casserole over a medium-high heat and brown the lamb until deeply golden all over, about 10-15 mins. Lift onto a plate, then tip the carrots, onions and rosemary stalks into the pan, and cook for 10 mins until just starting to colour. Pour in the wine, if using, and stock, and bring to a simmer. Nestle the lamb into the veg mixture, then cover and transfer to the oven for 3 hrs, turning the lamb once or twice until tender.
When the lamb is tender, lift it onto a board to rest. Strain the veg over a heatproof jug, reserving the roasting juices. Return the vegetables to the casserole. Spoon off as much fat as you can from the reserved roasting juices, then pour this over the veg along with the beans. Set the casserole over a low heat for 15-20 mins to warm the beans. When the beans are hot and the lamb has rested, carve the lamb into thick slices and serve with the beans, with the mint sauce on the side.