Drain tofu. Wrap block in a few layers of paper towels, then set it on a plate. Weigh it down with a heavy object, such as a skillet, pot, or large can, and let sit for at least 15 minutes to drain (see tip).
In small bowl, stir together miso, soy sauce, sesame oil, and ginger.
Slice tofu lengthwise into 2 pieces. Place tofu slices on baking sheet and brush on miso mixture. Bake for 20 minutes. Slice tofu into 1 inch cubes.
Meanwhile, bring large pot of water to a boil. Add soba and cook for 5 minutes, or until tender. In colander, drain well and then rinse with cold water.
In small bowl, place matcha, wasabi, and honey, add 2 Tbsp hot water and stir until contents of bowl are dissolved. Let cool and then stir in rice vinegar and lime zest. Taste and stir in additional wasabi, if desired.
Place soba noodles into serving bowls and drizzle on half of the matcha dressing. Add tofu, carrot, radish, mango, pea shoots, green onion, nori, and pickled ginger, if using, to bowl. Sprinkle on sesame seeds and drizzle on remaining dressing.