In a large saucepan or Dutch oven, add potatoes and 1 tablespoon salt. Add water to cover the potatoes by 1-inch, and bring to a boil over high heat. Reduce the heat to medium and simmer until the potatoes are tender (about 10 minutes). Reserve ½ cup of the potato cooking water, then drain the potatoes; return the potatoes to the pot and cover to keep warm.
While the potatoes are simmering, cook the bacon in a 12-inch skillet over medium-heat, stirring occasionally, until brown and crispy, 5 to 7 minutes. Using a slotted spoon, transfer the bacon to a paper towel-lined plate; pour off all but ¼ cup bacon fat. Add onion to the skillet and cook, stirring occasionally, until softened and beginning to brown, about 4 minutes. Stir in the sugar until it has dissolved, about 30 seconds. Add the vinegar and reserved potato cooking water; bring to a simmer and cook until the mixture is reduced to about 1 cup, about 3 minutes. Off heat, whisk in the mustard and pepper. Add the potatoes, parsley and bacon to the skillet and toss to combine; season with salt to taste. Serve warm.
Notes
If preparing this recipe as gluten-free, just be sure to use brands of bacon and whole grain mustard that are known to be GF.