Cook egg noodles in a large saucepan of boiling water for 5 to 7 minutes, or until al dente. Drain and set aside.
Heat the oil in a large frying pan over medium heat and cook gyoza until golden brown, turning once or twice. Add the water to the pan, reduce heat to low, cover and cook for another 3 minutes, or until liquid has evaporated. Rinse with cold water to cool, drain and cut gyoza in half.
In a large mixing bowl, toss together the water chestnuts, baby corn, carrot, mushrooms, peanut sauce, noodles and gyoza. Chill 1 hour. Toss with peanuts just before serving.