Combine the first 6 ingredients in a small bowl. Store in the fridge until needed. Heat your deep fryer to 350 degrees F. Cut the tofu into 3/4" cubes, set on paper towel, and gently pat the cubes dry. Spread the cornstarch on a plate. Coat the tofu in the cornstarch. Deep-fry until lightly golden brown, about 2 to 3 minutes, and then drain well. Arrange the tofu on a platter with ginger sauce alongside for dipping. Sprinkle with green onions and serve.
Note: Toast the sesame seeds in a small skillet set over medium heat. Swirl the pan occasionally, until the seeds are lightly toasted, about 5 minutes.