Cut the potatoes for the mash into rough 5cm chunks. Put them in a pan of cold, salted water, bring to a simmer and cook for 30 minutes. Drain well, then pass through a mouli, adding the butter. Put the potatoes back into the pan, season and add warm milk.
Place a large, shallow pan over a high heat. Add the oil and once it is hot, add the lamb mince. Spread it out evenly over the pan and leave it to cook for 3-4 minutes without stirring. When you see the meat beginning to colour around the edges, start to stir it and move it around the pan. Cook for another 5 minutes, adding half the salt and stirring every so often until the meat is golden all over. Tap the mince so it breaks down, then drain it in a colander set over a bowl to collect the oil.
Pour the oil back into the pan with butter. Add the diced carrot and the rest of the salt and cook on a low heat for 2-3 minutes, scraping all the sediment from the pan. Add the onion, garlic, thyme and dried herbs and cook for 3 minutes over a medium heat. Put the mince back in the pan with the flour. Cook this for a minute, then add the diced tomatoes, tomato purèe and stock and bring to a simmer.
Add the pepper and continue to simmer for 10 minutes. Pile the meat into a heatproof dish.
Place the cut potato into the cold water with 10g salt in a pan, place on to the heat and bring to a simmer turn the heat down and simmer for 30 minutes then tip the potatoes into a colander to drain really well.
Place the potato back in the pan and dry out on a low heat for 1 minute then add the butter, salt,pepper and the warm milk while you mash the potato.
Cover the Shepherd’s Pie mix with potato. Put the dish under a hot grill for 3 minutes to colour the top and the pie is ready.