Combine the truffle peelings and Madeira in a small saucepan over medium heat. Bring to a simmer. Simmer for 5 minutes. Strain through a fine sieve, separately reserving the liquid and peelings.
Heat 2 tablespoons of olive oil in the same saucepan over medium heat. Add the chopped onion, 1/4 cup of the chopped carrot, celery, and sachet. Saute for about 4 minutes, or until the vegetables are tender. Add the reserved Madeira liquid and stir to de-glaze the pan. Continue to cook for about 3 minutes or until the pan is almost dry. Add the rich chicken stock and cook about 4 minutes or until the liquid is reduced by half. Immediately strain through a fine sieve into a medium size, heat-proof bowl. Discard the solids. Set the liquid aside to cool.
When the liquid is cool, whisk in the vinegar, 1/2 cup of the remaining olive oil, and the truffle oil. Season the truffle vinaigrette to taste with salt and pepper. Set aside.
Remove the green part from the leeks (you may want to reserve this for making stock). Split leeks in half, lengthwise, down to but not through the root ends. Holding the leeks together by the root, rinse thoroughly under cold running water to remove all the grit. Pat dry.
Place the leeks in a medium saucepan along with the chicken stock, butter, minced parsley, and salt and pepper to taste. Bring to a simmer over medium-high heat. Lower the heat and simmer for 15 minutes or until the leeks are soft. Add the 1/2 cup of remaining diced carrots and simmer for 3 minutes. Cover and turn off the heat, but leave the pan on the burner to keep the leeks warm until ready to serve.
While the leeks are cooking, prepare the halibut.
Lightly season each piece of halibut with salt and freshly ground white pepper to taste. Place 2 truffle slices and 1 tarragon leaf on each side of the halibut. Using a large pastry brush, very lightly coat one side of 6 10-inch by 10-inch squares of plastic wrap with the remaining 1 tablespoon of olive oil. Securely wrap each piece of fish in an oiled plastic wrap square. Place the halibut in the top half of a steamer over lightly simmering water. Cover and steam for 8 minutes per inch, or until the fish is just firm but slightly underdone in the center. Remove the fish from the steamer.
Whisk the fines herbs into the reserved truffle vinaigrette.
Spoon equal portions of the melted leeks into the center of each 6 warm dinner plates. Unwrap the fish and place one piece on top of the leeks. Drizzle the vinaigrette over the fish and around the edge of the plate. Garnish top with crispy leeks and serve.
Add oil to deep fryer, or a 3-inch deep saute pan. Heat over medium-high until very hot but not smoking, and add the leeks. Quickly fry until the leeks are crisp, about 30 seconds. Remove leeks from oil immediately. Drain on paper towels and sprinkle with salt.