Place your skillet over medium heat, and pour oil in while preheating. Also, start water to boil according to package directions for your ramen. Chop up your vegetables into bite sized pieces while you wait.
Once pan is up to temperature, add the carrots (or tougher vegetables) first, and then layer with cabbage and zucchini (or softer vegetables), and finally add the precooked chicken. Pour small amount of sauces, up to a quarter cup, over the vegetable mixture, stir to coat, and cook until vegetables are soft but still with some bite. This usually takes between 5-10 minutes. Try not to over-stir while everything cooks!
While you are waiting for the vegetable mixture to cook, prepare the ramen according to the package directions. When finished, drain out much of the water. The ramen should be ready just as the vegetables are ready!
Turn the skillet onto low heat. Then using a pair of tongs, add the ramen to the skillet, pour over remaining sauces, and mix everything together.
Once everything is combined and evenly incorporated, serve up in bowls, and enjoy immediately!