Heat grill. Place green beans in medium microwave-safe bowl with 1 tablespoon water. Microwave on HIGH for 4 to 6 minutes or until crisp-tender; drain. Set aside.
Place potatoes in large bowl. Add 1 tablespoon of the salad dressing; toss to coat. Spoon potatoes into grill basket.
When ready to grill, place grill basket on gas grill over medium heat or on charcoal grill 4 to 6 inches from medium coals. Cook 15 to 20 minutes or until potatoes are tender, stirring occasionally. During last 5 minutes of cooking time, stir onion into potatoes.
In large bowl, combine cooked green beans, potatoes, onion and remaining salad dressing; mix well. Sprinkle with parsley. Serve immediately, or cover and refrigerate 1 hour to chill before serving.