Make the Teriyaki Sauce:

1. Combine Sauce Ingredients: In a small bowl, whisk together soy sauce, honey (or maple syrup), rice vinegar, water, sesame oil, minced garlic, and grated ginger. Mix until smooth.
2. Thicken the Sauce: In a small saucepan, bring the sauce mixture to a simmer over medium heat. In a separate bowl, mix the cornstarch with 1 tablespoon of cold water to create a slurry. Slowly add the slurry to the sauce, stirring constantly until it thickens. Remove from heat and set aside.

Cook the Chicken:

3. Prepare the Chicken: Slice the chicken breasts into thin strips. Season lightly with salt and pepper.
4. Cook the Chicken: In a large pan or skillet, heat the sesame oil and olive oil over medium heat. Add the sliced chicken and cook for 6-8 minutes, stirring occasionally, until the chicken is fully cooked and browned. Remove from the pan and set aside.

Cook the Noodles:

5. Prepare the Noodles: While the chicken is cooking, bring a pot of salted water to a boil. Cook the noodles according to package instructions (usually about 5-7 minutes). Drain and set aside.
6. Toss the Noodles: In the same pan you used to cook the chicken, add a little more sesame oil, if needed, and stir-fry the cooked noodles for 2-3 minutes until they are heated through and lightly crispy on the edges.

Assemble the Dish:

7. Combine the Ingredients: Return the cooked chicken to the pan with the noodles. Pour the teriyaki sauce over the noodles and chicken, stirring to coat everything evenly.
8. Garnish and Serve: Sprinkle sesame seeds and sliced green onions on top of the dish for added texture and freshness. Serve immediately.