As directed on the package, cook the pasta.
Combine cornstarch, soy sauce, and sesame oil in a small bowl. Stir in one tbsp sesame oil. Transfer the chicken to a large resealable plastic bag, seal the bag, and let stand for 10 minutes.
Place vinegar, sugar, soy sauce, and sesame oil in a small bowl; mix well.
Cook the chicken in canola oil in a large nonstick skillet until the juices run clear. Remove the chicken to a platter and keep it warm.
Add green onions, ginger, and pepper flakes to the same skillet as the peas and carrots and stir-fry for 5 minutes.
Add soy sauce mixture to chicken in pan; mix well. Stir pasta and sauce together in a skillet after draining.
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