Pour half the vegetable oil into a frying pan, season the lamb pieces and fry for five minutes until caramelised all over.
While the lamb is cooking, in a separate oven-proof casserole, add the remaining oil and fry the onions and carrots for 3-4 minutes until browned. Add the tomato puree and cook for a further two minutes.
Drain the lamb in a colander. Pour the white wine into the frying pan, bring to the boil, scrape off the sediment from the bottom of the pan, add to the vegetables.
Add the lamb, garlic, tomatoes, herbs and stock to the casserole. The liquid should just cover the meat (add extra stock if it doesn't). Bring to the boil and place a circular piece of baking parchment over the lamb and vegetables. Cover with a lid and cook at 180°C for 11/2-2 hours or until lamb is tender. Season to taste.
Once the lamb casserole is cooked, take out of the oven and leave to cool for one hour. Carefully transfer the lamb pieces into an oven-proof large frying pan, making sure they are not piled on top of each other. Strain the cooking liquid through a fine sieve placed over a saucepan, discard the vegetables. Ladle some of the liquid over the meat, bring to the boil and place in the oven at 200°C for 10-15 minutes, occasionally spooning the juices over the meat. As the liquid reduces it will become rich and sticky, intensifying the flavours and coating the pieces of lamb.
Heat the remaining sauce and reduce by a third.
Place the potatoes and vegetables into a pan, add 100ml of water, the butter, season and warm through. Once the pieces of lamb are shiny and glazed, place 4 or 5 pieces onto a bowl, spoon some of the vegetables on top, pour over the reduced sauce.
To make the mint sauce, place the mint, sugar and a pinch of salt in a pestle and mortar, pound into a paste, add the vinegar and oil. Drizzle over the dish.