Score the skin of each duck breast through to the flesh 4 times and rub generously with salt and pepper. Heat a heavy-based frying pan or ridged griddle pan until hot, add the duck breasts, skin side down, and cook for 3 minutes or until the skin is crispy. Drain off all the fat from the pan.
Transfer the duck to a roasting tin, skin side down, and brush with 1 tablespoon of the honey. Roast in a preheated oven, 200°C (400°F), Gas Mark 6, for 5 minutes or until cooked but still slightly pink inside. Remove from the oven and leave to rest for 3 minutes, then slice diagonally.
Meanwhile, add the wine, lime rind and juice, stock, ginger and remaining honey to the frying pan, bring to the boil and cook for 5 minutes. If using, blend the arrowroot with the measurement water in a cup and add to the sauce. Return to the boil, stirring continuously, and cook until thickened. Serve the duck with steamed chantenay carrots, sugar snap peas and asparagus, with the sauce drizzled over the top of the duck.