Scrub potatoes thoroughly with a stiff brush. In a large saucepan, cover potatoes with cold water. Cover and bring to boiling over high heat. Reduce heat; simmer for 15 to 20 minutes or until just tender.
Drain potatoes. Allow to cool until easy to handle (about 15 minutes). Cut into halves or quarters. Arrange in a shallow dish. Sprinkle with green pepper, green onions, and parsley.
In a small bowl, whisk together oil, vinegar, mustard, sugar, salt, and pepper. Pour over potatoes while still warm; toss gently. Let stand at room temperature for 1 hour before serving.
If you like, sprinkle crumbled bacon over potatoes before serving. Makes 8 servings.
You can cover and refrigerate the salad for several hours or overnight. Remove from refrigerator 1 hour before serving.