Step 1Place the carrots and carrot juice in a medium pot and bring to a simmer. Cook over low heat until the carrots are soft, about 10 minutes.
Step 2Pour the cooked carrots and juice into a blender. Add the ginger and lemon juice and blend at high until very smooth in consistency. Slowly add the olive oil while the blender is running. (Once the oil is added the color of the mixture will lighten, and it will get very creamy.) Season with salt and pepper and reserve warm. Makes about 1 cup.
Step 1Heat 1 tablespoon of the sesame oil over medium heat in a small saucepan. Add the daikon and sweat briefly, about 2 minutes.
Step 2Add the water chestnuts and vinegar and cook until the vinegar is reduced by half, about 4 minutes.
Step 3Add the remaining sesame oil and the chopped hijiki, season with salt and pepper. Reserve warm. This will have a salsa-like consistency. Makes about one-half cup.
Step 1Combine the olive oil, ginger, lemon grass and cilantro in a wide-based pot. Heat the oil to 160 degrees and maintain for 20 minutes.
Step 2Cool the oil to 125 degrees and maintain at 120 degrees while poaching the fish. The oil should have the feel of a hot bath.
Step 3Add the yellowtail portions, using the ginger, lemon grass and cilantro to keep the fish from the bottom of the pan.
Step 4Cook for approximately 15 minutes, or until the fish is slightly opaque and, if pinched, starting to fall apart. It is easiest to tell if the fish is done by touch, if you slightly squeeze it and it doesn't start to flake it isn't done, but it should not feel firm; it will be very soft. The resulting texture is extremely tender and silky.
Step 5Remove from the oil, blot and season with salt and pepper. For each serving, spoon carrot puree into the bottom of a soup bowl or ridged dinner plate. Place a piece of fish in the center of the plate. Spoon the vinaigrette on top and sprinkle with the edamame.