In a large pot, bring salted water to a boil. Add the baby potatoes and cook for about 15 minutes, or until tender. Drain and let cool slightly.
In the same pot of boiling water, add the green beans and cook for about 3-4 minutes until bright green and tender-crisp. Drain and immediately transfer to a bowl of ice water to stop the cooking process. Drain again after a few minutes.
In a large mixing bowl, combine the cooled potatoes, green beans, red onion, and parsley.
In a small bowl, whisk together the olive oil, red wine vinegar, Dijon mustard, salt, and pepper.
Pour the dressing over the salad and toss gently to combine. Adjust seasoning if necessary.
Chill the salad in the refrigerator for at least 30 minutes before serving to allow the flavors to meld.