1. Place the lamb cutlets in a shallow dish. Mix together the mint sauce, honey and oil and pour over the lamb. Set aside.
2. Peel the potatoes, carrots and swede. Cut the swede and the potato into 2 1/2 cm (1 inch) chunks and the carrots into 1 cm (1/2 inch) pieces.
3. Place in a large saucepan and cover with water. Add a pinch of salt, bring to the boil and cook for 10 minutes until tender. Drain well and return to the pan.
4. Meanwhile, trim the leeks and discard the coarse outer leaves. Slice lengthways and rinse to flush out any trapped earth. Shake off excess water and shred finely.
5. Melt half the butter in a large frying pan and stir-fry the leek for 3-4 minutes until just tender. Drain and keep warm.
6. Whilst the leeks are cooking, preheat the grill to a hot setting. Drain the lamb and arrange on the grill rack. Cook for 4-5 minutes on each side or until cooked to your liking - lamb is traditionally served slightly pink.
7. To serve, mash the root vegetables with a potato masher and mix in the remaining butter. Season. Pile on to four warmed serving plates.
8. Form the cooked leeks into small mounds on the plates, and top each with two lamb cutlets.
9. Grind over some pepper and garnish with mint.