Preheat the oven to 400°F. In a medium skillet set over medium heat, fry the bacon until the fat is rendered and the meat is just beginning to crisp, 8 to 10 minutes. Using a slotted spoon, transfer the bacon to paper towels to drain; reserve.
Discard all but about 1 tablespoon of the bacon fat from the pan. Add the olive oil and place over medium heat. When the combined fats are hot, add the leeks and sprinkle with salt and pepper. Cook until the leeks are very soft and beginning to meld together, about 20 minutes.
Meanwhile, roll out the puff pastry according to package directions and cut into 10 equal squares. When the leeks are done, spoon a bit onto each square and top with a sprinkling of the bacon. Transfer the tartlets to the oven and bake as directed on the pastry package until golden brown.