In a deep dish prepare a marinade by mixing oil, mustard, honey, salt and pepper. Marinate the duck breasts for 2 hours in the fridge, turning them 2 or 3 times. Drain them and put them to cook in a casserole, 5 minutes on the skin side and 3 minutes on the other. Take them out and keep them warm.
Degrease the casserole dish without washing it, add the juice from the marinade and the broth. Scrape the juices from the bottom of the casserole with the wooden spoon and let the sauce reduce for 5 minutes over high heat.
Cut the duck breasts diagonally. They should be pink. Arrange them on a heated dish and cover them with the sauce. Serve hot.
Accompany the duck breasts with small new turnips blanched then browned in butter and glazed with sugar.
