Peel the chestnuts and cook in salted water for about 10 minutes, then drain. Clean and wash the Brussels sprouts. Sauté in 1 tbsp. hot butter, salt. Deglaze with 400 ml water, cover and cook for about 15 minutes.
Wash the duck fillets and pat them dry. Cut the skin into a diamond shape, season. In a hot frying pan without fat, first fry them on the skin side for about 5 minutes. Then fry the meat side briefly. Place in an ovenproof dish with the skin facing upwards. Pour some of the resulting frying fat on. Roast in a hot oven (electric cooker: 200 °C/recirculating air: 175 °C/gas: level 3) for 15-20 minutes
Pour the remaining fat out of the pan, except for 1-2 tablespoons. Peel the shallots and cut into slices. Sauté in hot frying fat. Sprinkle with sugar and lightly caramelise. Deglaze with vinegar and port wine. Glaze and season the chestnuts for about 5 minutes, turning them frequently.
Remove the meat and let it rest in aluminium foil for about 5 minutes. Stir 2 tablespoons of butter in pieces into the chestnuts, season to taste. Cut open the duck breast. Serve everything. Goes well with croquettes