Cook potatoes in a Dutch oven in boiling water to cover 15 to 18 minutes or until tender; drain and cool slightly. Cut into bite-size pieces. Drizzle potatoes with rice vinegar; toss gently.
Snap off tough ends of asparagus, and discard; cut asparagus and green beans into 1-inch pieces. Cook asparagus and green beans in boiling water to cover 3 minutes or until crisp-tender; drain. Plunge into ice water to stop the cooking process; drain and add to potato mixture. Add onion and next 3 ingredients; toss gently.
Whisk together mustard and next 4 ingredients; gradually whisk in oil until blended. Drizzle over potato mixture; toss gently. Sprinkle with parsley.