In a large skillet heat the 1 tablespoon oil over medium heat. Add chicken; cook 15 minutes or until done (165 degrees F), turning once. Meanwhile, in a food processor or blender combine half of the spinach, 1/2 cup of the walnuts, the 1/2 cup oil, the garlic, and salt. Cover and process until smooth.
Transfer chicken to a cutting board; cover to keep warm. Add the water to the skillet. Bring to boiling. Break up noodles and add to skillet (discard seasoning packets). Cook 5 minutes, stirring occasionally to break up noodles. Stir in remaining spinach and the spinach pesto until spinach is wilted. Remove from heat.
Cut chicken into bite-size strips. Stir into noodle mixture. Top with the remaining nuts, the Parmesan cheese, crushed red pepper, and, if desired, lemon zest.