Cook noodles according to package directions; drain and set aside.
Prepare dressing: In a blender container, combine the 1/2 tablespoon of olive oil, the vinegar, peanut butter, soy sauce, honey, gingerroot and crushed red pepper flakes; process until smooth.
Heat the 1 teaspoon of olive oil and the sesame oil in a large skillet over medium-high heat. Add bell pepper strips and green onions; cook and stir for 1 to 2 minutes or until green onions are nearly transparent; remove from skillet and set aside.
Add chicken strips to the skillet and stir-fry for 2 to 3 minutes or until cooked through. Return vegetables to the skillet and add cooked noodles; cook and stir for 1 minute or until heated through; remove skillet from the heat and pour the dressing over the chicken/veggie mixture; toss lightly to coat.
Divide chicken mixture evenly among dinner plates and sprinkle with cashews.