Combine chicken broth, peanut butter, soy sauce, honey and ground red pepper in a small bowl; whisk and set aside (it's ok if it's not smooth).
Heat 2 teaspoons of the oil in a stir-fry pan or large skillet over high heat. Add chicken, 1 teaspoon of the gingerroot and 1 minced garlic clove. Cook and stir 6-7 minutes or until the chicken is no longer pink. Remove from the skillet; keep warm (I just put it on a plate).
Reduce heat to medium-high. Heat remaining 2 teaspoons oil in the same skillet. Add broccoli, celery (if using) and remaining gingerroot and garlic. Cook and stir 2 minutes or until vegetables are crisp-tender. Return chicken to skillet. Stir in sauce; bring to a boil. Remove skillet from heat.
Meanwhile, bring 4 cups water to a boil in a small pot (2-quarts is great). Break noodles and add to boiling water (discard seasoning packets). Cook 3 minutes, stirring occasionally; drain. Stir noodles into chicken mixture. Sprinkle with cashews or peanuts. Serve immediately.