1. Bring potatoes to a boil in a large pot of boiling water. Cover, reduce heat to medium, and cook 20 to 30 minutes, or until tender; drain. Cut into 1-inch pieces, if needed. Place in large bowl along with onions, peperoncini, and parsley. Do not mix at this point.
2. In a small bowl, combine olive oil, vinegar, salt, and pepper. Beat with a fork to blend. Toss potatoes gently with dressing. Season with additional salt, if needed. Chill.