Flour, for dusting
1 (17-ounce) package frozen all-butter puff pastry, thawed overnight in the refrigerator
1 cup shredded sharp white cheddar cheese
1/2 cup crème fraîche or sour cream
2 tablespoons coarsely chopped chives
12 thin slices pancetta or bacon (optional)
1 tablespoon olive oil
6 large eggs
Kosher salt, to taste
Freshly ground black pepper, to taste
Heat the oven to 400°F and arrange a rack in the middle. Line a baking sheet with parchment paper.
On a lightly floured work surface, roll out the sheet of puff pastry into a rectangle about 14 inches by 12 inches. Trim all of the edges. Cut the rolled-out sheet into 6 equal rectangles.
Using a fork, prick the pastry all over. Place the rectangles on the prepared baking sheet and chill for 15 minutes.
In a bowl, stir together the cheese, crème fraîche, and half the chives.
In a large nonstick frying pan, fry the pancetta (if using) over medium-low heat until just crisp, about 5 minutes. Drain on paper towels. Discard the fat in the pan and reserve the pan.
Dollop a spoonful of the cheese mixture into the center of each chilled pastry rectangle, dividing the mixture evenly among the rectangles and spreading it out nearly to the edge.
Roughly chop the pancetta and sprinkle it over the cheese mixture.
Bake until the pastry is puffed, crisp, and golden, about 15 minutes.
While the puff pastry is baking, fry the eggs: In the reserved frying pan, warm the olive oil over medium-low heat. Crack the eggs into the pan and season with salt and pepper. Cover the pan and cook until the whites are cooked through and the yolks are still a bit runny.
Place the warm tartlets on warm plates and top each with a fried egg. Sprinkle with the remaining chives and serve.
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