How to Make It
Spread the diced tofu on a paper towel–lined plate to drain for 20 minutes.
Meanwhile, in a large pot of boiling water, cook the soba noodles until tender, about 5 minutes. Drain and rinse under cold water until cool; drain again. Transfer the noodles to a large bowl and toss with 2 teaspoons of the vegetable oil.
In a small, heatproof bowl, combine the scallions with the ginger, sesame seeds and salt. In a small saucepan, heat the remaining 3 tablespoons plus 1 teaspoon of vegetable oil over moderately high heat until shimmering. Pour the hot oil over the scallion mixture. Stir in the rice vinegar and sesame oil. Pour the dressing over the noodles and toss to coat. Add the tofu and watercress, toss gently and serve.