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1
Heat the oven to 400 degrees F and arrange a rack in the middle.
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2
Line a baking sheet with parchment paper.
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3
On a lightly floured work surface, roll out the sheet of puff pastry into a rectangle about 14 inches by 12 inches.
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4
Trim all of the edges.
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5
Cut the rolled-out sheet into 6 equal rectangles.
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6
Using a fork, prick the pastry all over.
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7
Place the rectangles on the prepared baking sheet and chill for 15 minutes.
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8
In a bowl, stir together the cheese, creme fraiche, and half the chives.
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9
In a large nonstick frying pan, fry the pancetta (if using) over medium-low heat until just crisp, about 5 minutes.
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10
Drain on paper towels.
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11
Discard the fat in the pan and reserve the pan.
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12
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.
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13
Roughly chop the pancetta and sprinkle it over the cheese mixture.
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14
Bake until the pastry is puffed, crisp, and golden, about 15 minutes.
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15
While the puff pastry is baking, fry the eggs: In the reserved frying pan, warm the olive oil over medium-low heat.
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16
Crack the eggs into the pan and season with salt and pepper.
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17
Cover the pan and cook until the whites are cooked through and the yolks are still a bit runny.
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18
Place the warm tartlets on warm plates and top each with a fried egg.
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19
Sprinkle with the remaining chives and serve.
