Put the potatoes in a medium saucepan and cover with cold water. Cover, bring to a boil, then reduce the heat to medium, cover partially, and cook until a fork or knife glides easily into the potatoes, about 15 minutes.  Drain the potatoes, but don’t rinse them, and let cool in the colander 6 to 8 minutes.

While the potatoes are cooking, put the eggs in a small saucepan and cover with cold water. Bring to a boil, then remove from the heat, cover and let stand for 7 minutes. Drain, then return them to the pot and cover with cold water to cool them; change the water a few times, and when they are cool enough to handle, peel and chop the eggs (peeling them under water helps get the shells off cleanly).

And still, while both the potatoes and eggs are cooking, in a small bowl, combine the mayonnaise, mustard, vinegar, scallions, red onion, parsley, sugar, and salt and pepper to taste.

Transfer the potatoes to a large bowl and the chopped cooked eggs. Pour in the dressing, and add half the bacon. Toss well to combine. Top with the rest of the bacon, and serve at room temperature.