Bring a large pot of water to a boil, salt it, add the noodles and cook until al dente. Drain thoroughly.
While the pasta is working, in a large skillet, add the vegetable oil, 2 turns of the pan, over medium-high heat. Toss the chicken with the ginger; season with pepper. Add the chicken to the hot skillet in an even layer and let it brown up, 4 to 5 minutes.
Shake and stir the skillet to turn the chicken pieces, then add the scallions, tamari, sugar and sesame oil. Simmer for 1 minute.
Add the pasta to the skillet and toss to combine. To serve, transfer to serving bowls and sprinkle with toasted sesame seeds.