Cook noodles according to package directions. Meanwhile, combine soy sauce, sesame oil, vinegar, garlic, ginger, and crushed red pepper. Set 2 tablespoons of the soy sauce mixture aside. Drain noodles. In a large bowl toss noodles with the remaining soy sauce mixture. Place noodle mixture in freezer to quick chill.
Rinse chicken; pat dry. Grill chicken on the lightly greased rack of an uncovered grill directly over medium heat for 12 to 15 minutes or until an instant read thermometer inserted near the center registers 170 degree F, turning once and brush occasionally with the reserved soy sauce mixture. For the last 8 minutes of grilling, place eggplant slices on the rack alongside the chicken; turn once and brush occasionally with reserved soy sauce mixture. Transfer chicken and eggplant to cutting board; cool for 5 minutes and cut into cubes.
Toss chicken, eggplant, and cabbage with noodles. Sprinkle with cashews (if desired) and cilantro. Makes 4 servings.