Heat the oil in a saucepan, add the onion, carrot, celery and thyme and cook gently for 10 minutes until soft and golden.
Add the minced lamb and cook over a high heat, breaking up with a wooden spoon, for 5 minutes until browned. Add the tomatoes, tomato purée and salt and pepper to taste. Bring to the boil, then reduce the heat, cover and simmer for 30 minutes.
Remove the lid and cook for a further 15 minutes until thickened.
Meanwhile, put the potatoes in a large saucepan of lightly salted water and bring to the boil. Reduce the heat and simmer for 15–20 minutes until really tender. Drain well and return to the pan. Mash in the butter, milk and half the cheese and season to taste with salt and pepper.
Spoon the minced lamb mixture into a 2 litre (3½ pint) baking dish and carefully spoon the mash over the top, spreading over the surface of the filling. Fork the top of the mash and scatter over the remaining cheese. Bake in a preheated oven, 190°C (375°F), Gas Mark 5, for 20–25 minutes until bubbling and golden.