In a large saucepan, bring 2 quarts of water to a boil. Slightly break up noodles from both ramen packages (throw away one of the seasoning packets and keep one to use later) and add to water, along with vegetables. Return to boiling and reduce heat a bit. Boil gently, uncovered for 3 minutes (don't overcook!). Drain and return to saucepan.
Meanwhile, make your sauce by whisking together water, peanut butter, soy sauce, brown sugar, cornstarch, crushed red pepper and 1 seasoning packet from the ramen. Whisk until smooth.
Cook and stir over medium heat until thickened and bubbly. Cook and stir for 2 minutes more.
Add chicken, water chestnuts and bamboo shoots to sauce. Heat through. Add to noodle and vegetable mixture in saucepan. Toss to combine.
Place in bowls and top with chopped peanuts and sliced green onions. Serve immediately and enjoy!