Prepare all vegetables by slicing the onion into 1/4-inch thin strips, slicing celery on the bias, julienning carrots into 2-inch matchsticks, and cutting broccoli into florets. Shred the cabbage and set all vegetables aside. Cut the chicken into 1/2-inch bite-sized cubes and place in a bowl. Add the 2 tablespoons teriyaki sauce, grated ginger, minced garlic, and 0.75 teaspoon corn starch to the chicken, mixing well to coat evenly. Let the chicken marinate while you prepare the remaining components—this brief marination will help infuse flavor even if you skip the full hour chill time. In a separate small bowl, whisk together the 1/3 cup teriyaki sauce, 2 teaspoons corn starch, sesame oil, and red pepper flakes; set aside.

Bring a large pot of salted water to a boil and add the pasta. Cook for 3 minutes to achieve a slightly underdone texture—this is important because the noodles will continue cooking when tossed with the hot sauce and chicken in the final step. Drain the pasta thoroughly and set aside, tossing lightly with a small drizzle of oil to prevent sticking.

Heat 2 tablespoons of high-smoke-point oil in a large wok or skillet over medium-high heat until shimmering. Once the pan is hot, carefully add the marinated chicken from Step 1 in a single layer and let it sear without stirring for about 1-2 minutes to develop color and flavor. Stir and continue cooking for another 2-3 minutes until the chicken is mostly cooked through but still tender. Transfer the cooked chicken to a clean plate and set aside.

Add the remaining 1 tablespoon of oil to the same wok over medium-high heat. Add the sliced onion, celery, and carrots from Step 1 and stir-fry for 2-3 minutes until they begin to soften and develop color—I like to keep these vegetables with a little snap rather than cooking them until completely tender, as they'll continue softening with the sauce. Add the broccoli florets and shredded cabbage to the wok and stir-fry for another 3-4 minutes until the cabbage begins to wilt and the broccoli is tender-crisp.

Return the cooked chicken from Step 3 to the wok with the vegetables. Add the cooked pasta from Step 2 and pour in the teriyaki sauce mixture prepared in Step 1. Toss everything together over medium-high heat for 2-3 minutes, stirring constantly so the sauce coats all components evenly and thickens slightly. I recommend giving everything a good toss to ensure the noodles aren't clumped together—the slight undercooking of the pasta is now an asset as it finishes cooking in the residual heat and absorbs the sauce flavor.

Divide the teriyaki chicken chow mein into bowls or plates. Serve immediately while hot, ensuring each portion has a good mix of noodles, chicken, and vegetables with plenty of the glossy teriyaki glaze.