How to Make It
In a small saucepan, combine the honey wine with 1/4 cup plus 1 tablespoon of the white port, the demi-glace and the lemon juice and bring to a boil. Simmer over moderate heat until reduced to 1/3 cup, about 10 minutes. Whisk in 1 tablespoon of the butter and the chestnut honey and season with salt and black pepper.
Preheat the broiler. Heat a large skillet. Add the duck, skin side down, and cook over moderate heat until the skin is golden and crisp, 15 minutes; spoon off the fat as it accumulates in the skillet. Season the duck, then turn the breasts skin side up and cook for 7 minutes longer for medium-rare. Transfer the duck to a rimmed baking sheet, skin side up, and sprinkle with the chopped Jordan almonds, pressing to adhere.
Transfer the duck to the center of the oven and broil for about 2 minutes, or until the sugar is caramelized; turn the baking sheet as necessary for even browning. Let the duck breasts rest before slicing.
In a medium skillet, melt the remaining 2 tablespoons of butter. Add the chanterelles and cook over moderately high heat, stirring occasionally, until their liquid has evaporated and they are lightly browned, about 8 minutes. Season the chanterelles with salt and black pepper, add the shallot and cook for 1 minute longer.
In a large bowl, whisk the walnut, grapeseed and hazelnut oils with the vinegar and the remaining 1 tablespoon of white port. Stir in the parsley. Add the frisée and chanterelles, season with salt and cayenne pepper and toss to coat. Mound the salad on plates. Reheat the honey wine sauce. Cut the duck breasts crosswise into 1/2-inch slices and arrange them next to the salad. Drizzle the sauce all around and serve.
Honey wine, also called mead, is available at most liquor stores. Duck-and-veal demi-glace and veal demi-glace are available at specialty food shops and from D'Artagnan (800-327-8246 or dartagnan.com).
Boiled baby turnips or radishes sautéed in butter.