1. Place the potatoes, salt, and water to cover in a large saucepan or Dutch oven; bring to a boil over high heat, then reduce the heat to medium and simmer until the potatoes are tender (a thin-bladed paring knife can be slipped into an out of the potatoes with little resistance), about 10 minutes.  Reserve 1/4 cup potato cooking water, then drain the potatoes; return the potatoes to the pot and keep warm.

2. While the potatoes are cooking, fry the bacon in a large skillet over medium heat, stirring occasionally, until browned and crisp, about 5 minutes.  With a slotted spoon, transfer the bacon to a paper-towel-lined plate; pour off all but 2 tablespoons bacon grease.

3. Add the onion to the skillet and cook, stirring occasionally, over medium heat until softened and beginning to brown, about 4 minutes.  Stir in the sugar until 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 1/2 cup, about 3 minutes.  

4. Off the heat, whisk in the mustard and pepper.  Add the potatoes, parsley, and bacon to the skillet and toss to combine; adjust the seasonings with salt to taste.  Transfer to a bowl and serve immediately, while still warm.