Boil water in a large pot and cook the spaghetti according to the package instructions. Drain and set aside.
In a wok or large skillet, heat the vegetable oil over medium-high heat.
Add the sliced chicken and cook for about 5-7 minutes, or until fully cooked, stirring frequently.
Add the minced garlic to the chicken and sauté for another minute.
Add the sliced red and green bell peppers, julienned carrot, and broccoli florets to the chicken. Stir-fry for about 3-4 minutes until the vegetables are tender-crisp.
In a small bowl, mix together the soy sauce, oyster sauce (if using), and sesame oil. Pour this sauce over the chicken and vegetables, stirring to coat evenly.
Add the cooked spaghetti to the wok and toss everything together until well combined. Season with salt and pepper to taste.
Remove from heat and garnish with chopped green onions and sesame seeds if desired.