Cover the potatoes in water and bring to a boil. Cook until the potatoes can be easily pierced with a knife, about 20 minutes. Drain and allow to cool. Cut the potatoes into quarters.
Cut pieces of bacon crosswise into ½” strips and fry until crisp in a large frying pan. Using a slotted spoon, remove the bacon from the pan to drain on a paper towel. Reserve about 2 tablespoons of the bacon fat in the pan and pour off the rest.
Add the diced red onion to the pan with the bacon fat and cook over medium heat until the onion begins to soften. When the onions are soft and starting to color, add the vinegar and whole grain mustard to the pan and cook for 3-4 minutes. Mix in the salt, sugar and black pepper.
Add the cooked potatoes to the pan with the dressing and toss gently with a large spoon to combine. Remove the pan from the heat.
Mix in the crisp cooked bacon, the sliced green onion and the chopped parsley. Serve immediately while still warm. The salad can also be served room temperature or cold.