Cook egg noodles in a large pot 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, cook potstickers 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 in half.
In a large mixing bowl, toss together the water chestnuts, baby corn, carrot, mushrooms, peanut sauce, noodles and potstickers. Chill 1 hour. Toss with peanuts just before serving.
Vegetable potstickers and straw mushrooms are available at Chinese/Oriental speciality stores.