Fill a large saucepan with water, add the potatoes and bring to a boil over medium-high heat. Lower to a simmer and cook about 20 minutes. Potatoes should only be parboiled at this point. Drain. Transfer to a small baking sheet and freeze for 1 hour.
Meanwhile, cook the bacon in a large skillet until crispy and most of the fat has been rendered, about 10 to 12 minutes. Transfer to a paper towel and crumble. Pour the bacon fat from the pan into a heatproof bowl and set aside.
Whisk together 3 Tbsp. of the vinegar and the mustard in a small bowl. Slowly stream in 1/4 cup of the hot bacon fat, whisking until well blended. Season with salt and pepper.
Remove the potatoes from the freezer and cut into 1/2-inch cubes.
Pour about 1-1/2 inches of water and the remaining vinegar into a large skillet and bring to a slow simmer.
Meanwhile, heat 3 Tbsp. 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, about 5 minutes.
Then add the potatoes. Season liberally with salt and pepper and saute until the potatoes are just cooked through, stirring frequently, about 5 minutes. Turn the heat to medium-high and continue cooking until the potatoes are browned and crispy, stirring frequently, about 8 minutes longer.
Transfer the potatoes to a preheated 400-degree 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, for 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.