For the five spice blend: In a small pan over low heat, combine the spices and toast until very fragrant, about 2 to 3 minutes. Transfer to a spice grinder and blend to a powder; reserve.
For the eggplant caponata: Preheat oven to 400°F. In a large sauté pan over medium-low heat, warm the olive oil. Add the eggplant with a sprinkling of salt and cook, stirring, for four minutes. Add the onion, garlic, tomato, olives, capers, and raisins. Cook, stirring occasionally, until the mixture begins to soften and blend, about 15 minutes. Add the vinegar, place in the oven and cook for 20 minutes, stirring occasionally. (If the caponata seems too dry, add water as needed.) Season to taste and keep warm.
For the lamb: While the caponata is cooking, season the lamb on all sides with salt and pepper. In a large sauté pan over high heat, sear the lamb in olive oil on all sides until browned. Remove from the pan and coat evenly with the five-spice mixture. Place lamb on a rack, and roast in the 400°F oven about 10 minutes, until lamb reaches an internal temperature of 130°F. Remove and rest at room temperature for about five minutes.
To serve: Slice the lamb racks between every two bones. Serve two slices per person, with the eggplant caponata.
For the lime gelée: Soak the gelatin sheets in cold water for 20 minutes. In a small saucepot over low heat, dissolve the sugar in the lime juice. Remove the gelatin sheets from the water, squeeze out excess water, and then dissolve completely in the hot lime juice. Strain through a fine-mesh sieve and transfer to a shallow, flat container. Chill in the freezer until set, about 15 minutes, then cut into desired shapes.
For the carrot and ginger purée: In a large sauté pan over medium-low heat, add the olive oil, carrots, onions, leeks, ginger, and a pinch of salt. Cook, stirring, for about 15 minutes, or until very tender. Transfer the vegetables to a blender with the lime juice and puree, adding the carrot juice gradually until the texture is smooth and thick, like a loose mayonnaise. Season with salt, pepper, and lime juice to taste.
Finish the dish: Slice the Kona Kampachi very thinly, against the grain of the fish. Skin the avocado, remove the pit, and slice; season with lime juice, and salt and pepper to taste. Arrange the sliced fish onto 4 to 6 chilled plates in a decorative fashion, garnishing each with lime gelée, carrot puree, avocado, and micro cilantro.