Preheat the oven to 425 degrees, then line two sheet pans with parchment paper.
Toss the potatoes with 1 tablespoon olive oil, salt, and pepper, then arrange on one sheet pan.
Place the bacon pieces on the other sheet pan, then place both in the oven.
Cook bacon until crisp, about 10-15 minutes, then remove from the pan and drain on paper towels. Reserve 2 tablespoons of bacon fat.
Cook the potatoes, tossing once or twice about halfway through, until golden and crisp, about 20-25 minutes.
Place a wide pot of water on the stove and bring up to a simmer.
Add minced shallots, Dijon mustard and white wine vinegar to a small bowl or jar and whisk to combine.
Season with salt and pepper, then slowly whisk in remaining 2 tablespoons of olive oil and reserved bacon fat until emulsified.
Taste for seasoning and adjust as needed.
Crack one egg into a small dish, then use a large spoon to create a whirlpool in the simmering water.
Carefully slide the egg into the center and use the back of the spoon to keep the whites together as much as possible.
Repeat with the remaining egg. Cook for approximately 3-4 minutes, or until the whites are set but the yolks are still runny.
Remove with a slotted spoon, then drain very well on a towel.
Add the frisee lettuce to a large bowl, then toss with vinaigrette until fully coated.
Divide between two plates, then top each with potatoes and bacon, then place the poached eggs on top.
Season with more salt and pepper, then serve immediately.