Clean and wash the Brussels sprouts. Heat 1 tablespoon butter. Sauté the sprouts briefly in it. Deglaze with approx. 400 ml salt water and cook covered for approx. 16 minutes. Wash duck breast and dab dry.
Incise skin diamond-shaped. Season vigorously with salt and pepper. In a pan without fat, fry for approx. 5 minutes on the skin side first. Then turn and fry briefly on the meat side.
Place in an ovenproof dish with the skin side facing upwards. Pour on some of the roast stock. Roast in the preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: level 3) for 10-15 minutes. Peel the shallots and cut into fine strips.
Pour the rest of the stock out of the pan. Heat the pan. Brown the shallots in it. Sprinkle with sugar and allow to caramelize slightly. Deglaze with vinegar and port wine. Add chestnuts, bring to the boil and cook for 5-10 minutes, turning.
Remove the meat, wrap it in foil and let it rest for about 5 minutes. Add 30 g butter in pieces to the chestnuts and stir in. Season to taste with salt and pepper. Cut open the duck breast. Arrange everything.
Garnish with thyme. Croquettes are delicious with it.