In a blender, puree the soy sauce with the rice vinegar, mirin, sake, mustard and one-third of the garlic. With the machine on, slowly pour in 6 tablespoons of the vegetable oil and blend until smooth.
Using a mandoline, thinly slice half of the cucumber lengthwise. Finely julienne the remaining cucumber half as well as the carrot and daikon. In a medium bowl, toss the julienned vegetables together.
In a large skillet, heat the remaining 3 tablespoons of vegetable oil. Add the sliced shallot and the remaining garlic and cook over moderate heat until golden brown, about 3 minutes. With a slotted spoon, transfer the shallot and garlic to a paper towel–lined plate to drain.
Season the grouper fillets with salt and pepper and add them to the skillet. Cook over moderately high heat until browned on the bottom, about 4 minutes. Turn and cook over moderate heat until just white throughout, about 2 minutes longer.
Spoon 1 tablespoon of the soy-mustard dressing in the center of each plate. Fold the cucumber slices and arrange them on the dressing. Set the grouper fillets on the cucumbers, browned sides up, and top with the julienned vegetables. Drizzle with the remaining dressing. Garnish with the fried garlic and shallot, the chile strips, toasted sesame seeds, cilantro leaves and chives and serve right away.