For the demi-glace bones wash and dab dry. Peel, wash and roughly dice the carrots, celery and onions. Heat the oil in a large frying pan. Fry the bones over high heat until brown, turning them over.
Add the vegetables and onions and fry. Stir in tomato paste and sweat it.
Deglaze with wine and about 4 l of water so that the bones are covered. Bring to the boil and simmer at low heat for about 6 hours until thick. Use a skimmer to remove any foam that develops.
Wash the thyme and add the spices (except salt) about 1 hour before the end of cooking. Pour the demi-glace through a fine sieve (= pass through). Season to taste with salt.
Preheat oven (electric cooker: 100 °C/circulating air: not suitable/gas: see manufacturer). Wash duck breasts, dab dry and cut the skin several times. In a pan without fat, first fry on the skin side for approx. 5 minutes, then on the meat side for 1-2 minutes.
Season with salt and pepper. Remove from the pan and cook in the hot oven for about 30 minutes. Pour off frying fat up to approx. 2 tbsp., set the pan aside.
For the sauce, halve the pomegranates. Remove the seeds from 2 halves and press out 2 halves. Wash the thyme, dab dry, chop and sauté in cooking fat. Deglaze with 200 ml demi-glace and pomegranate juice.
Bring to the boil and simmer for about 10 minutes. Add pomegranate seeds. Season to taste with salt, pepper and sugar.
Cut the duck breast open and serve with the sauce. Serve with green beans tossed in thyme-shallots butter.