Heat the oil in a large frying pan and put in the duck breasts skin side down. Gently saute for 5 minutes, until they have released some of their fat.
Add the onion, sprinkle with salt and pepper, and continue to fry gently until soft, stirring from time to time.
When the duck breasts are brown on the skin side turn them over then turn again when the flesh is lightly coloured. Remove from the pan when they are still underdone and set aside.
Strain off the duck fat and return the onions to the frying pan. Add the pomegranate molasses, the walnuts and about 4 fl oz water. Stir well and add sugar to taste.
Return the duck breasts to the pan and simmer gently in the sauce until they are done. Serve immediately.