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.