Place a large pot of water over high heat for the noodles. Once boiling, add some salt and the noodles and cook according to the package directions. Drain thoroughly.
While the water is coming up to a boil, place a large skillet over medium-high heat with the vegetable oil, about two turns of the pan. Toss the chicken with the grated ginger and season with some pepper. Add the chicken to the hot skillet; spread it out in an even layer and let it brown up for a couple of minutes.
Shake and stir the skillet to turn the chicken pieces, then add the scallions, Tamari (eyeball it), sugar and sesame oil; bring up to a bubble and simmer for 1 minute.
Add the drained noodles to the skillet and toss to combine. To serve, transfer to serving bowls and sprinkle with some of the toasted sesame seeds.