Put the potatoes in a large pot and cover them with at least one inch of cold water. Add a generous tablespoon of salt and bring the pot to a boil. Cook for about 10 minutes, until a fork slides in easily.
Drain the potatoes well in a colander. While they are still warm, cut them into thick discs or chunks. Warm potatoes soak up the dressing better than cold ones, so set them aside and keep them close.
Cook the bacon in a large skillet over medium-high heat until crispy. Lift it out with a slotted spoon and let it drain. Keep at least two tablespoons of the drippings in the pan, then crumble the bacon once it cools a little.
Lower the heat to medium and add the chopped onion to the bacon drippings. Cook for 5 to 8 minutes, stirring now and then. You want the onion soft and just starting to turn golden.
Pour in the vinegar and water, then add the sugar, salt, pepper, celery seeds, and mustard. Stir well and bring it to a boil. The smell at this point is sharp, sweet, and smoky all at once.
Add the sliced potatoes, parsley, and half of the crumbled bacon to the skillet. Toss gently until every piece is coated and heated through. Move it to a serving bowl, then top with the rest of the bacon and a little more parsley.