Bring a pot of salted water to a boil and cook the noodles according to package instructions until al dente. Once cooked, drain thoroughly and set aside.
Cut the chicken breast into bite-sized cubes and place in a mixing bowl. Add the chopped garlic, ginger, and soy sauce. Season with salt and pepper, stir well to coat, and let it marinate while preparing the vegetables.
Peel the carrot and dice it into small, uniform pieces. Dice the zucchini as well to ensure even cooking.
In a skillet or wok, heat the oil over medium-high heat. Add the diced carrot and zucchini to the hot pan and stir-fry for around 5 minutes until the vegetables begin to soften but still retain some crunch.
Add the marinated chicken to the pan along with any leftover marinade. Cook, stirring occasionally, for 8 to 10 minutes or until the chicken is fully cooked and lightly browned.
Add the drained noodles to the skillet. Toss everything together until well combined and heated through. Taste and adjust seasoning with salt if needed.
Transfer to serving plates while hot. Garnish with a generous sprinkle of sesame seeds and freshly chopped parsley before serving.