Press the extra firm tofu for 15 minutes to remove excess moisture, then cut into 1/2-inch cubes.
Bring a pot of water to a boil and cook the soba noodles according to package directions. Drain and rinse under cold water until chilled.
Heat half of the toasted sesame oil in a non-stick skillet over medium-high heat. Add tofu cubes and sear until golden brown and crispy on all sides, about 8-10 minutes.
While tofu cooks, use a vegetable peeler to shave the English cucumber and carrots into long, thin ribbons. Stop when you reach the watery core of the cucumber.
Thaw the shelled edamame by rinsing under warm water or steaming briefly, then set aside.
In a small bowl, whisk together the remaining sesame oil, rice vinegar, tamari, grated fresh ginger, minced garlic, and red pepper flakes.
In a large mixing bowl, combine the chilled soba noodles, cucumber ribbons, carrot ribbons, and edamame.
Pour the dressing over the salad and toss gently to coat all ingredients evenly.
Divide the salad into bowls and top with the warm crispy tofu.
Garnish with sliced green onions and black sesame seeds before serving.