Bring lightly salted water to a boil in a large saucepan. Add noodles and carrots, return to boiling and cook 5 minutes. Stir in edamame and snow peas; cook, uncovered, for 3 to 5 minutes longer or until noodles and vegetables are tender. Drain and return to saucepan.
In a medium bowl, mix together peanut sauce, peanut butter, and soy sauce until it's smooth. Stir the peanut sauce into pan with the noodles and veggies. Sprinkle on the cilantro and peanuts. Serve family-style, and let kids spoon their helping into a bowl.