Preheat the oven to 350 degrees. In a spice grinder, grind the star anise pods and black peppercorns to a powder. Transfer the powder to a small bowl and stir in the sugar, cinnamon and cardamom.

Heat a large ovenproof skillet. Season the duck breasts with salt and generously sprinkle them with the spice mixture. Add the duck breasts to the skillet, skin side down. Cook over moderate heat until the skin is browned and crisp, about 5 minutes. Turn the breasts and cook for about 2 minutes longer. Transfer the skillet to the oven and bake the duck breasts for about 5 minutes, until they are medium-rare. Transfer the duck breasts to a carving board and let rest for about 5 minutes. Thickly slice the duck, arrange the slices on plates and serve.