In a large pot, cook the noodles according to the package instructions. Once cooked, rinse under cold water (to prevent sticking) and set aside.
While the noodles cook, mix together the ingredients for the sauce in a small bowl. Set aside.
In a large skillet over medium heat, add 2 tablespoons oil. Cook the chicken about 3 minutes on each side, until cooked through. Drain any juices and set aside the cooked chicken.
Add 1 tablespoon of oil to the skillet. Add the carrots and bell pepper and cook for 8 - 10 minutes, until tender. Add the bean sprouts and cook for 2 minutes more.
Move the vegetables to create space in the middle of your pan. Add the 2 eggs and lightly scramble them. Set aside the cooked eggs and vegetables with the chicken.
Add the sauce to the pan over low heat. Bring to a boil and then simmer for 1 minute to thicken.
Add the chicken, vegetables, egg and noodles to the pan. Stir (using tongs if possible) until coated in the sauce.
Serve warm. Optionally, top with peanuts, cilantro, green onions, and red pepper (for spice).