1. Preheat the oven to Gas mark 9, 240C, 450F.
2. Place the racks, fat side up on a chopping board and lightly score. Season on both sides with salt, pepper and allspice and place in a large shallow dish.
3. Prepare the glaze; in a small bowl mix together the sugar, vinegar and rum. Pour over the racks, cover and leave to marinate for 20 minutes.
4. Heat the oil in a large non-stick frying pan under a moderate heat, remove the racks from the marinade and brown for 3-4 minutes on both sides.
5. Transfer the racks to a medium-sized roasting tin and roast for 5-15 minutes, depending on how your lamb is preferred. Cover the bones with foil if browning too quickly.
6. Meanwhile, prepare the tomato and courgette salsa; mix all the ingredients together into a large bowl, cover and set aside at room temperature until required.
7. Serve the racks with the salsa and a sweet potato gratin.