Set aside one seasoning packet from the ramen packages and discard the other packet.
In a large saucepan, bring 2 quarts of water to a boil. Break the noodles slightly and add them plus the cut vegetables to the boiling water.
Return to a boil, then reduce heat and simmer uncovered for 3 minutes until noodles and vegetables are tender. Drain well and return to the saucepan.
While noodles cook, make the sauce: in a medium saucepan whisk together 1 1/4 cups water (or coconut milk), peanut butter, soy sauce, brown sugar, cornstarch, crushed red pepper, and the reserved seasoning packet until smooth.
Cook the sauce over medium heat, stirring until it thickens and begins to bubble, then continue to cook and stir for 2 more minutes.
Stir the chopped cooked chicken, drained water chestnuts, and drained bamboo shoots into the sauce and heat through.
Pour the chicken and sauce mixture over the drained noodles and vegetables in the large saucepan and toss to combine evenly.
Serve topped with chopped peanuts and sliced green onions.