Scrub the potatoes under running water with a soft brush. Quarter them and drop them into a kettle of cold, salted water. Bring to a boil and cook until tender but still firm, 8 to 10 minutes after the water reaches a boil.
Meanwhile, chop the bacon and saute in a small skillet until crisp. Remove bacon and reserve.
In the bacon fat remaining in the skillet, saute chopped shallots until tender but not at all browned, 5 minutes or so. Reserve shallots and fat.
When the potatoes are done, drain them and drop them into a mixing bowl.
Pour vinegar, olive oil, shallots and reserved bacon fat over the still-hot potatoes. Season with salt and pepper to taste, and gently toss. Add purple onion and parsley and toss again. Cool to room temperature, cover, and refrigerate.
Before serving bring back to room temperature, toss, correct seasoning and add additional oil and vinegar if the salad seems dry. Sprinkle reserved crisp bacon on top.