Cook pasta according to package directions; drain and rinse with cold water. Drizzle with oil and toss to coat.
Place the lettuce in a 2-1/2-qt. glass serving bowl; top with pasta and eggs. Sprinkle with salt and pepper. Layer with chicken and peas. In a small bowl, mix dressing ingredients until blended; spread over top. Refrigerate, covered, for several hours or overnight.
Just before serving, sprinkle with cheese and parsley. Yield: 12 servings.