Cook the spaghetti noodles according to the package instructions, then drain and set aside.
Heat sesame oil in a large pan over medium heat and add the cubed chicken breast.
Cook until the chicken is browned and cooked through, about 5-7 minutes.
Add minced garlic and ginger to the pan, sautéing until fragrant, about 1 minute.
Add the red bell pepper and snow peas, cooking until they are just tender.
In a small bowl, combine soy sauce, hoisin sauce, brown sugar, and rice vinegar, mixing well.
Pour this sauce into the pan, tossing to coat the chicken and vegetables.
Add the cooked noodles to the pan, tossing everything together until evenly mixed.
Sprinkle sesame seeds and green onions on top before serving.