First, prepare the Ginger-Soy Sauce.
In a small bowl, whisk together the rice vinegar, toasted sesame oil, reduced-sodium soy sauce, minced garlic, grated ginger, and crushed red pepper flakes.
Set aside to let the flavors meld.
Cook the pasta in a large pot of boiling, lightly salted water according to the package directions.
Once cooked al dente, drain it well and immediately return it to the warm pot.
Cover to keep warm.
While the pasta cooks, combine the cubed tofu, chopped cucumber, carrot pieces, and sliced green onions in a large serving bowl.
Add the warm, drained pasta to the bowl with the tofu and vegetables.
Drizzle the prepared Ginger-Soy Sauce over everything and toss gently until all the are evenly coated.
Serve immediately or chilled.