Soak the noodles in room temperature water according to the instructions on the package. Transfer them to a colander to drain, then cut the noodles into shorter pieces and toss them with oil to prevent them from sticking.
Mix all of the ingredients for the sauce. Set aside.
Heat 1 tablespoon of oil in a non-stick skillet or wok over medium-high heat. Add the chicken and sauté for about 6 minutes until cooked. Transfer the chicken to a plate.
Add the remaining oil to the skillet. Add the garlic and sauté for about 1 minute, or until fragrant. Add the onions, carrots, tomato, cabbage, and white pepper to the skillet and stir-fry for about 2-3 minutes.
Move the vegetables to one side of the pan and add the beaten eggs to the empty side. Scramble the eggs until cooked.
Add the chicken, noodles, and sauce back to the skillet. Stir-fry until the noodles are soft and all the ingredients are combined and coated in the sauce.
Serve sprinkled with chopped green onions.