In a bowl, toss the diced chicken with chicken marinade ingredients. Set aside to lightly marinate while you chop and gather the remaining ingredients, about 10–15 minutes.
In a separate bowl, whisk together the soyaki ingredients. Set aside.
In a small bowl, mix the cornstarch with the cold water to create a slurry. Set aside.
Heat a large skillet over medium heat. Add the marinated chicken and cook until fully cooked through and lightly caramelized on the outside. Be careful not to let it burn or overcook. Remove the chicken from the skillet and set aside.
Cook the noodles according to the package directions. Drain and set aside. I usually undercook slightly and cook them when everything else is almost done.
Add a little oil to the skillet if needed. Add the veggies and cook just until slightly tender, but still crisp.
Add the fresh ginger and garlic to the skillet and cook until fragrant, about 30 seconds. Set veggies aside.
Pour in the Soyaki sauce and bring it to a gentle simmer.
Slowly stir in the cornstarch slurry, adding just enough to thicken the sauce into a glossy glaze.
Add the cooked chicken and veggies back into the skillet. Stir to coat everything in the sauce.
Add the cooked noodles and toss until everything is evenly coated and the sauce clings to the noodles.
Let everything cook together for another 1–2 minutes, until the noodles are sticky, glossy, and caramelized in the sauce.
Serve warm with green onions and toasted sesame seeds, if desired.