In a large pot of boiling salted water, cook 8 ounces trimmed green beans, cut into 2-inch pieces, until crisp-tender, about 4 minutes. Use a slotted spoon
to transfer to a colander. In same pot, cook 6 ounces soba noodles according to package instructions; drain well (do not rinse).
Meanwhile, cut 6 ounces firm silken tofu into 1/2-inch cubes; drain on paper towels. Place in a bowl. In another bowl, whisk together 3 tablespoons fresh lime juice, 2 tablespoons soy sauce, and 2 teaspoons toasted sesame oil. Pour half the dressing over tofu; toss gently to coat.
In a large bowl, toss remaining dressing with noodles, green beans, and 2 minced scallions. Sprinkle tofu on top. Let cool.