Put a 28cm-wide, heavy-based casserole pan on a medium-high heat. Heat 35g ghee until it’s searing hot, then brown the lamb on all sides in two or three batches, so as not to overcrowd the pan. Once seared and nicely coloured, transfer to a medium bowl and repeat with the remaining lamb.
Add the remaining 35g ghee to the pan with the onions and cook, stirring frequently, for 20 minutes, until softened and golden brown. Add the next eight ingredients, stir well and cook for another three to five minutes, until fragrant. Return the lamb and any juices from the bowl to the pan, then stir in the tomatoes, chicken stock and a teaspoon and a half of salt.
Add the potatoes and carrots to the pot, bring up to a hard simmer, then turn the heat down low, cover the pan and cook, stirring occasionally, for two and a half hours, until the meat is tender; take off the lid for the last 20 minutes, so the sauce thickens. Leave the curry to sit, uncovered, for 30 minutes, to give the flavours a chance to mingle.
Heat the oven to 220C (200C fan)/425F/gas 7. While the oven’s warming up, make the carrot sambal. Put the carrots, onions, vinegar, half a teaspoon of salt, the garlic, ginger, brown sugar and chilli in a bowl, toss to combine, then leave to steep for 30 minutes. Squeeze out the mixture with your hands, to remove as much excess liquid as possible, then mix with the remaining ingredients and the finely chopped coriander stalks.
While the carrot mix is pickling, make the curry leaf oil. In a small frying pan, heat the ghee on a medium heat and, once hot, add the curry leaves, fry for about five minutes, until dark green, then take off the heat and set aside.
Put the bread rolls on a medium oven tray, brush them all over with some of the curry leaf oil, then warm in the oven for five minutes. Cut off the tops of the rolls, like giving them little hats, then hollow out the rolls. Spoon in a generous amount of the curry, followed by some of the sambal, a spoonful of the ghee and some curry leaves. Pop the tops of the rolls back on and serve hot with the remaining curry leaves, coriander and condiments on the side.