Fill a large saucepan with cold water, add the potatoes and bring to a boil over medium-high heat. Lower to a simmer and cook until a fork pierces through the potatoes with a bit of resistance, about 20 minutes. The potatoes should only be par-boiled at this point. Drain, transfer to a small baking sheet, and freeze for 1 hour.
Meanwhile, make the vinaigrette for the potatoes. Cook the bacon in a large cast-iron skillet until crispy and most of the fat has been rendered, 10 to 12 minutes. Transfer to a paper-towel-lined plate and crumble. Pour the bacon fat from the pan into a heatproof bowl and set aside.
Whisk together 3 tablespoons of the vinegar and the mustard in a small bowl. Slowly stream in 1/4 cup of the hot bacon fat, whisking until emulsified. Season with salt and pepper.
Remove the potatoes from the freezer and cut into 1/2-inch cubes.
Preheat the oven to 400 degrees F. Pour about 1 1/2 inches of water and the remaining white distilled vinegar into a large straight-sided skillet and bring to a slow simmer.
Meanwhile, heat 3 tablespoons of the reserved bacon fat and the canola oil in the same skillet used for the bacon over medium heat. Add the red onions and cook until softened, 4 to 6 minutes, and then add the potatoes. Season liberally with salt and black pepper and saute until the potatoes are just cooked through, stirring frequently, 4 to 6 minutes. Turn the heat to medium high and continue cooking until the potatoes are browned and crispy, stirring frequently, 6 to 8 minutes longer. Transfer the potatoes into the oven while you poach the eggs.
Crack the eggs one at a time into a cup, and then carefully slide each into the simmering water. Cook until firm, turning occasionally with a slotted spoon, 3 to 5 minutes, and then transfer to a kitchen towel-lined plate with the slotted spoon. Sprinkle with salt and pepper.
Toss the potatoes with the mustard-bacon vinaigrette and serve topped with the poached eggs and garnished with the reserved bacon and chives.