In deep fat fryer or heavy saucepan, heat 3 inches vegetable oil to 375°F. Fry rice stick noodles in hot oil until they float on top of the oil and are curled up, less than 1 minute. Set aside.
Heat 10-inch skillet over medium heat. Sprinkle salt and pepper on both sides of chicken breasts. Drizzle 1 tablespoon olive oil in skillet. Cook chicken breasts in oil about 15 minutes or until browned on both sides and juice of chicken is clear when center of thickest part is cut (at least 165°F). Cut into slices.
On 2 salad plates, layer bok choy, chicken, bell pepper, green onions, cucumber and cashews.
In tightly covered container, shake dressing ingredients, or beat in small bowl with whisk. Pour dressing over salads.
Top with fried rice stick noodles, and serve.