In a medium saute pan, heat the sunflower oil over medium-high heat. Season the fillets with salt and pepper. Sear the fillets until golden brown on each side to the desired degree of doneness. Drain on a paper towel-lined plate.
Over high heat, heat a small non-stick pan or skillet. Season the slices of duck foie gras with salt and pepper. When the pan is very hot, put the slices of duck foie gras in it, and quickly sear for about 1 minute on each side. Drain on a paper towel-lined plate.
To serve, in the middle of each plate, arrange the bouquetiere of vegetables. On top of the vegetables, place a fillet. On the top of the fillets, put a slice of foie gras. On the top of the foie gras, add the slices of black truffle. Pour the sauce delicately around the vegetables.
Put the carrots in 1 saute pan and the turnips in another. Add water up to the top of the carrots, and add 2 tablespoons sugar and 1 tablespoon butter. Season with salt and pepper, and cook over medium-high heat until liquid is completely evaporated and vegetables are tender. To the other pan, add water up to the top of the turnips, and add 2 tablespoons sugar and 1 tablespoon butter. Season with salt and pepper, and cook over medium-high heat until liquid is completely evaporated and vegetables are tender. Remove vegetables, and then continue to cook until the remaining sugar and butter become a light caramel. When the caramel is at the right color (light brown), return the carrots and turnips to the respective pans until each vegetable gets the brightness and light brown color. Season the carrots and turnips individually. Divide 2 tablespoons of chopped parsley among the saute pans. Remove from heat and set aside.
To cook the string beans, bring a small pan full of water to boil. Add a large handful of sea salt. When the water is boiling, add the string beans and let them cook for about 10 to 15 minutes, until the string beans are soft and not 'crispy'. Refresh the string beans in cold water with the ice cubes. To reheat the string beans, melt some butter in a skillet or saute pan, add the string beans, and saute for 3 to 4 minutes. Add the chopped shallots and the remaining chopped parsley and saute for about 1 to 2 more minutes. Season, to taste.
Put the potatoes in a small pan. Add water up to the top of the potatoes. Add the sunflower oil and boil the potatoes and oil for about 2 to 3 minutes. Drain the potatoes.
In a skillet or a saute pan, heat the clarified butter over high heat until very hot. Carefully add potatoes and cook until golden brown. Season with salt, to taste. Drain the clarified butter from the pan. Add 2 tablespoons raw butter and cook again for 3 to 4 more minutes. Set aside and keep warm.
In small pan, put the shallots, garlic, bouquet garni, cracked black pepper, Madeira, and cognac. Bring to a boil and then simmer until the Madeira is completely evaporated. Add the brown stock and let it reduce by half. Strain the sauce through a fine-mesh strainer. Pour the sauce into a sauté pan. Add the foie gras and the finely chopped black truffle. Mount the sauce with butter, without a whisk, by moving the pan slowly over medium heat. Season, to taste. Set aside and keep warm in a bain marie.
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