Cook noodles according to package directions; drain and rinse under cold water. Set aside.
In a bowl, toss chicken with 1 tbsp soy sauce and cornstarch. Let stand 10 minutes.
In a small bowl, whisk together chicken broth, remaining 1 tbsp soy sauce, oyster sauce, rice vinegar, sesame oil, and red pepper flakes.
Heat 2 tbsp vegetable oil in a wok or large skillet over high heat. Add chicken in a single layer; cook without stirring 2 minutes until browned. Stir-fry 1-2 minutes more until cooked through. Transfer to a plate.
Reduce heat to medium-high. Add remaining 1 tbsp oil, garlic, and ginger; stir-fry 30 seconds. Add bell pepper, broccoli, and carrot; stir-fry 3-4 minutes until crisp-tender.
Return chicken to wok. Add noodles and sauce; toss to combine and heat through, about 2 minutes. Garnish with green onions.
Tips
Substitute chicken with shrimp, beef, or tofu.
For extra veggies, add snap peas or mushrooms.
Store leftovers in an airtight container in the refrigerator for up to 3 days.