Add the cubed potatoes to a large pot. Fill the pot with water so that it covers the potato by 1 inch.
Place the pot 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 fork-tender.
While the potatoes cook, Place a large, deep skillet over medium heat. Cook the bacon (in two batches) until crispy, flipping as needed. Transfer the bacon to a paper towel-lined plate and leave the drippings in the pan. Once cool enough to handle, chop the bacon into small pieces.
Add the onions to the bacon drippings and cook for about 5 minutes, stirring frequently, until softened.
Add the vinegar, brown sugar, and mustard to the skillet. Stir to combine, scraping the bottom of the pan to get the brown bits up. Let the sauce reduce slightly.
When the potatoes are cooked, drain the water, but do not rinse the potatoes. Add the potatoes, chopped bacon, and olive oil to the skillet with the onion sauce and stir to coat.
Transfer the potato salad to a large bowl. Sprinkle with parsley before serving warm.
Notes
If you don't have a deep-sided skillet, you can return the potatoes to the pot they were boiled in. Then add the bacon and dressing to the pot and mix everything together.
If using thick-cut bacon, you can reduce the amount to 6 slices. Or you can increase the amount of bacon all the way up to 1 pound.
Some people like to add garlic or celery to German potato salad. You can add 2 stalks of finely chopped celery to the skillet at the same time as the onions. Then you can add a minced garlic clove or two with 1 minute left on the onion cook time, but make sure to stir constantly so the garlic doesn’t burn.