To ensure paper-thin slices of daikon and lotus root, use a mandoline.
Place daikon and scallions in a large bowl filled with ice and water.
Whisk together mirin, vinegar, oils, and a generous pinch of salt.
Place cabbage in a large bowl, and toss with half of the dressing. Divide among plates. Top with 3 slices each daikon and lotus root, a tofu cube, and a fanned-out scallion half. Drizzle with remaining dressing.