For the eggplant:
Thinly slice eggplant into rounds about 1/4-inch thick. Toss liberally with salt.Place the eggplant in a perforated pan or bowl, and press with a weight. Allow eggplant to release its moisture overnight.
Remove eggplant from container and discard water. Toss liberally with champagne vinegar and allow to sit overnight.
Drain excess vinegar from eggplant and toss with a handful of raw garlic cloves, and 3-4 stems of fresh rosemary and fresh thyme. Cover with extra virgin olive oil and refrigerate. Eggplant can be kept covered in oil and refrigerated for up to 2 months.
For the brovada:
Using a sharp knife or mandoline, thinly slice the baby turnips into 1/8-inch rounds. In a mixing bowl, combine the 1/4 cup water, vinegar, sugar, salt and crushed grapes then pour over turnips. Cover and refrigerate for 48 hours.
For the duck:
Preheat the oven to 325F.
Separate the legs and breasts from the duck carcass. Pull off the loose fat from the duck pieces and carcass and set aside.
In a small saucepan, combine the reserved duck fat and 1/4 cup water and cook over low heat until the water has evaporated and the fat is liquefied, about 1 hour. Place the duck legs in a shallow, nonreactive casserole and cover with the hot fat. Cover and bake for 2 hours. Keeping the oven on, remove the duck and allow it to cool. (The legs may be stored in the refrigerator, covered in the fat, for up to 4 weeks.)
Remove the legs from the cooked fat and wipe off the excess fat with a paper towel. Season the breasts and legs well with salt and pepper.
In a 12- to 14-inch ovenproof sauté pan, heat 1 tablespoon of the olive oil over high heat until smoking. Add the legs and sauté them, skin side down, until the skin is crispy. Remove the pan from the heat and place it in the oven to heat through, for about 5 minutes.
In a second sauté pan of equal size, heat 1 tablespoon of the olive oil until smoking. Add the breasts, skin side down, and sear them over high heat, draining the excess fat from the pan when necessary. When the skin is crispy, turn the breasts and cook on the flesh side until they are medium rare, or approximately 130F. Transfer the breast to a cutting board and allow them to rest for 5 minutes, then slice on a bias.
In a small sauté pan, gently warm the eggplant with some of its oil, discarding the whole garlic and herbs. Toss in a handful of the thinly sliced radicchio and season with salt and pepper.
Mound the eggplant and radicchio in the center of the warmed dinner plate. Top with the crispy duck leg and fan the sliced breast atop the leg. Finish with the marinated turnips and dress the meat lightly with the reserved turnip pickling liquid.