Dice 4 tablespoons of butter and freeze. Dab meat dry and season with pepper. Wrap ham slices around the fillets. Preheat oven (electric cooker: 100°C/circulating air: 75°C/gas: see manufacturer). Heat 2 tablespoons of oil in a frying pan.
Brown the fillets in it all around for 8-10 minutes at medium heat. Place in an ovenproof dish. Cook in a hot oven for about 1-1 1/4 hours. Put the pan with the frying fat aside.
Clean and wash spring onions and cut them into 2-3 pieces depending on their length. Cut pomegranates in half. Squeeze 1 pomegranate on a citrus press. Remove the seeds from the second one. Wash the thyme, dab dry and remove the leaves.
Peel, wash and cut the potatoes into pieces. Cover and cook in boiling salted water for about 20 minutes.
Heat 1 tablespoon of oil in a second pan. Sauté the spring onions all around. Season with salt and pepper. Take out, keep warm. Heat 2 tbsp. butter in a frying pan. Sauté the sesame seeds in it.
Drain the potatoes. Add milk and tahini and mash everything finely. Season to taste with salt.
Heat up the frying fat from the fillet again. Deglaze with 1/8 l water and dissolve the frying set. Add pomegranate juice and thyme and bring to the boil. Remove from the heat and gradually beat the frozen butter into the sauce until it is lightly thickened.
Season to taste with salt, pepper and cumin. Stir in pomegranate seeds. Cut meat into slices. Serve with sauce, spring onions and puree. Drizzle the sesame butter over the puree.