Place the port in a large saucepan and bring to a boil over high heat. Continue to cook until the port has reduced to a thick glaze about 1/3 to 1/2 cup in volume and is thick enough to coat the back of a spoon, about 20 minutes. (Be especially careful near the end of the cooking time, as it is easy to burn the glaze near the end.) Transfer to a nonreactive, heatproof bowl and set aside to cool to room temperature before proceeding.
Preheat the oven to 275 degrees F.
Using a boning knife, remove the duck meat from the carcasses so that you have 4 halves, each with the wing and leg bones still attached. Cut the wing tips off and reserve for the duck jus along with the duck carcasses. Season the duck halves on both sides with 2 teaspoons of salt, the Essence, and the black pepper. Place on a rimmed baking sheet, skin sides up, and drizzle each duck with about 1 1/2 tablespoons of the port wine glaze. Rub the shallots with the olive oil and season with the remaining 1/2 teaspoon salt and the white pepper and add to the baking sheet. Place the baking sheet in the oven and cook until the shallots are golden brown and tender, 45 minutes to 1 hour, depending on the size of the shallots. Remove the shallots and keep warm until ready to serve. Continue roasting the duck until tender and golden brown, about 2 hours in total. Remove from the oven and let rest a few minutes before serving.
When ready to serve, spoon some of the Pureed Sweet Potatoes onto each of 4 plates and top each plate with half a duck. Divide the roasted shallots evenly among the plates, then drizzle some of the Duck Jus around the edge of each plate. Drizzle some of the remaining port wine glaze over each plate, then top with a few haricots verts. Serve immediately.
Combine all ingredients thoroughly.
Recipe from "New New Orleans Cooking", by Emeril Lagasse and Jessie Tirsch, published by William Morrow, 1993.
Break and crack the carcasses. In a large stockpot, heat the vegetable oil. Season the bones with salt and pepper. Add the bones to the pot and brown for about 10 minutes, stirring often. Add the onions, carrots, celery, garlic, and bay leaves. Season the mixture lightly with salt. Cook until the vegetables are soft, about 5 minutes, stirring often. Add the wine and tomato paste and stir to mix. Cook for 5 minutes, stirring occasionally. Add the water. Put the thyme, parsley sprigs, and peppercorns in a piece of cheesecloth, tie it together with kitchen twine, and add it to the mixture. Bring the mixture to a boil. Skim off any cloudy scum that rises to the surface. Reduce the heat to medium and simmer, uncovered, for 3 hours. Strain through a fine-mesh strainer and discard solids. Reserve half of the stock for another purpose. Place the remaining stock in a saucepan, bring to a boil, and reduce until stock is very rich and flavorful and reduced in volume to about 1/2 cup. Set aside until ready to serve the duck. (The leftover stock can be stored in the freezer for 1 month.)
Place potatoes in a medium saucepan and add enough cold water to cover by 2 inches. Bring to a boil over high heat. Reduce the heat so that the potatoes remain at a low boil and cook until fork tender, about 10 minutes. Drain in a colander placed in the sink.
Transfer the potatoes to the bowl of a food processor along with all remaining ingredients and process until fairly smooth, 1 to 2 minutes. Return the potato puree to the saucepan and warm gently over low heat, stirring frequently, before serving.
Bring a small saucepan of salted water to a boil. Add the haricots verts and cook until just tender, about 1 minute. Transfer with a slotted spoon to an ice bath to refresh. Drain. In a large skillet, melt the butter over medium-high heat. Add the drained haricots verts, and cook, stirring, for 3 minutes, or until warmed through but still crisp-tender.