Poach the chicken and cool in its own liquids; save excess stock for another use and chop or pull the meat. Or, remove rotisserie chicken meat from the bones and skin and chop or pull the meat.
Par-boil the broccoli in a few inches of salted water for 5 minutes and drain.
Cook the white or brown rice according to the package directions or cook the egg pasta.
In a small pot, loosen the cashew butter over low heat, then add the ginger, garlic, Sriracha, lime juice, stock, soy sauce and hoisin and season with black pepper. Bring to a bubble, then simmer to let the sauce thicken and the flavors combine.
Heat the oil over high heat in large skillet. Add the onions, peppers and broccoli, and stir fry to tender crisp. Add the water chestnuts, sauce and chicken; combine and season, to taste. Serve over rice or toss with long egg noodles; garnish with cashews, scallions and cilantro.