1. Bring the lamb racks to room temperature by removing from the fridge half an hour before cooking, and halve them to make serving easier. Rub racks with a little oil and season well with salt and pepper.
2. Put the oil in a large, non-stick baking dish and add the carrots, garlic cloves and thyme or rosemary leaves. Toss to coat and sprinkle salt on top. Place lamb racks on top of the carrots, pushing down so they touch the bottom of the dish.
3. Place the baking dish in the middle of a very hot barbecue with heat surrounding it on both sides, but not directly underneath. Close the hood and cook for about 15–20 minutes, until the lamb is medium–rare or done to your liking. Remove the lamb to a warm bowl and set aside to rest, loosely covered, for about 10 minutes.
4. Continue cooking the carrots for another 15–20 minutes until slightly crunchy and caramelised, then remove from the barbecue. Either place them in a serving bowl and return lamb racks to the baking dish and place both dishes in the middle of the table, or place a rack of four cutlets and several carrots onto each (warm) serving plate.