Step 1: Cook ramen noodles according to package directions until slightly al dente. Drain well, toss with 1 tablespoon of sesame oil to prevent sticking, and set aside.
Step 2: Pat chicken pieces dry with paper towels. Season lightly with salt and black pepper.
Step 3: In a small bowl, whisk together soy sauce, brown sugar, rice vinegar, 1 teaspoon sesame oil, and cornstarch for the stir-fry sauce. Set aside.
Step 4: Heat 1 tablespoon of cooking oil in a large wok or large non-stick skillet over medium-high heat. Add chicken pieces and stir-fry for 3-5 minutes, until golden brown and cooked through. Remove chicken from the wok and set aside.
Step 5: Add the remaining 1 tablespoon of cooking oil to the wok, if needed. Add minced garlic and grated ginger and stir-fry for 30 seconds until fragrant.
Step 6: Add broccoli florets, sliced carrots, and red bell pepper to the wok. Stir-fry for 3-4 minutes, until vegetables are tender-crisp.
Step 7: Add snap peas (or snow peas) and stir-fry for another 1-2 minutes until vibrant.
Step 8: Return the cooked chicken to the wok with the vegetables.
Step 9: Whisk the stir-fry sauce again and pour it over the chicken and vegetables. Cook, stirring constantly, for 1-2 minutes, until the sauce thickens and coats everything.
Step 10: Add the cooked ramen noodles to the wok. Use tongs to toss everything together gently, ensuring the noodles are fully coated with the sauce and mixed with the chicken and vegetables. Cook for another 1-2 minutes to heat through.
Step 11: Remove from heat. Garnish with sliced green onions and sesame seeds, if desired. Serve immediately.