Position a rack in the middle of the oven and preheat to 400°F (200°C). Line a baking sheet with parchment paper.
On a lightly floured work surface, roll out the pastry into a rectangle about 12 by 15 inches (30 by 38 cm). Trim the edges (I like to use a pizza wheel and a ruler to cut puff pastry). Cut the rectangle into 6 equal rectangles, each about 5 by 6 inches (13 by 15 cm). Using a small, sharp knife, cut a line around each rectangle about 1/2 inch (12 mm) from the edge. Do not cut all the way through; you just want to create a ridge when the pastry is baked. Using a fork, prick the pastry inside the line all over. Lay the rectangles on the prepared baking sheet. Refrigerate while you prepare the toppings.
In a small bowl, stir together the shredded cheese and crème fraîche. In a large frying pan (it is best to choose a nonstick pan with a lid, so you only have to clean one pan), fry the bacon over medium-low heat until just barely crisped, about 5 minutes. Drain on paper towels. Discard the fat in the pan.
Dollop a spoonful of the cheese mixture in the center of each pastry rectangle and spread it out to the cut line. Roughly chop the bacon and sprinkle it over the cheese mixture. Bake until the pastry is puffed, crisp, and golden, about 15 minutes.
While the pastry is baking, fry the eggs: In the large frying pan, warm the olive oil over medium-low heat. Crack the eggs into the pan. Sprinkle with salt and a few grinds of pepper. Cover the pan (this is a handy trick for making beautiful over-easy eggs) and cook until the whites are cooked through and the yolks are still a bit runny.
Place the tarts on warmed plates and top each with a fried egg. Sprinkle with chives and serve.
This breakfast recipe is excerpted with permission from <a href="http://www.amazon.com/gp/product/1616282002/ref=as_li_qf_sp_asin_il_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=1616282002&linkCode=as2&tag=craftfocom-20">"Home Baked Comfort (Williams-Sonoma): Featuring Mouthwatering Recipes and Tales of the Sweet Life with Favorites from Bakers Across the Country"</a> by Kim Laidlaw and published by Weldon Owen.