Combine the mustard, vegetable, and extra-virgin olive oils in a cup with a pour spout.
In a mixing bowl, combine the wasabi, lemon juice, rice vinegar, Dijon mustard, yuzu kosho, and soy sauce, and whisk well. Slowly add the oils, whisking constantly to emulsify. Taste for seasoning, add salt, and set aside.
Place tuna in a glass or stainless steel bowl. Add the shallots and chives, and toss gently to combine. Drizzle about half of the vinaigrette over the tuna, and mix well. Let the tartar sit for 2 minutes; taste for seasoning, and add more of the vinaigrette or salt, to taste. Leftover vinaigrette will keep, refrigerated, for 1 week.
To serve: shape 1/6 of the tuna tartar into a disc and place it in the center of a serving plate. Arrange 3 dollops of seaweed salad around the disc and garnish with 3 potato slices. Top tuna with a small spoonful of caviar, if desired.
Sesame Seaweed Salad:
Place the wakame in a mixing bowl, and soak it in tepid water for 20 to30 minutes. Remove from water, squeeze dry, and trim away the tough spine. Cut into thin strips, and place in a large mixing bowl.
In a separate bowl, combine the vinegar, salt, sugar, and both oils. Pour the dressing over the wakame, add the chile peppers, and toss. Sprinkle with the sesame seeds.
Preheat an oven to 350 degrees. Peel the potatoes, and using a mandolin for best results (you can thinly slice with a knife, but you will not get the criss-cross pattern which makes these potatoes unique), slice them thin in a criss-cross pattern with the zig-zag part of a mandolin. Lay the slices onto a non-stick sheet pan, not overlapping, and brush them with clarified butter. Bake until crisp, about 12 minutes.