Whisk ginger, miso paste, 3 Tbsp. mirin, 3 Tbsp. vinegar, 1 Tbsp. soy sauce, and 1/4 tsp. salt in a large bowl.
Cook soba noodles according to package directions. Drain noodles, rinse with cold water, then add to ginger mixture. Season with more mirin, vinegar, soy sauce, and salt, if needed.
Transfer noodles to a serving bowl or platter and top with radishes, scallions, and tofu. Serve immediately.
