In a deep dish, whisk together the olive oil, violet mustard from Brive, chestnut honey, salt, and pepper to create a flavorful marinade. Coat the duck breasts thoroughly and marinate in the fridge for 2 hours, turning 2-3 times for even flavor infusion.
Drain the breasts and sear in a casserole over medium-high heat: 5 minutes skin-side down for crispy perfection, then 3 minutes on the other side. Remove and keep warm under foil.
Degrease the casserole without washing. Add the marinade juices and chicken broth. Scrape up the flavorful browned bits with a wooden spoon, then reduce the sauce over high heat for 5 minutes until glossy and thickened.
Slice the duck breasts diagonally—they should be beautifully pink inside. Arrange on a warmed platter, drizzle with the sauce, and serve hot. Pair with blanched baby turnips sautéed in butter and glazed with a touch of sugar for an authentic French touch.
