Add the cubed potatoes to a large pot and fill with water about 1 inch over the top of the potatoes.
Heat the potatoes over medium-high heat and bring to a boil, then reduce heat to a simmer and cook for about 20 minutes until the potatoes are just fork-tender.
Meanwhile, cook the bacon in a large, deep skillet in two separate batches until crisp. Transfer the bacon to a paper towel-lined plate and leave the drippings in the pan. Chop the bacon once cool enough to handle.
Add the onions to the drippings and cook for about 5 minutes, stirring frequently.
Add the vinegar, sugar, and mustard and stir to combine, scraping the bottom of the pan to get the brown bits off. Let the mixture reduce slightly.
When the potatoes are cooked, drain but do not rinse. Then add the potatoes, chopped bacon, and olive oil to the skillet with the onion mixture and stir to combine.
Add parsley then serve warm.