How to Make It
In a small saucepan, cover the potatoes with cold water and bring to a boil. Cook over high heat until tender when pierced with a knife, about 15 minutes. Drain, then peel and thinly slice crosswise.
Meanwhile, in a medium skillet, cook the bacon over moderately high heat until crisp, about 5 minutes; transfer to paper towels. Cut the slices in thirds.
Preheat the oven to 375°. Pour off the bacon fat in the skillet and add the oil. Add the onion and cook over moderate heat, stirring frequently, until softened and browned, about 15 minutes; add water as necessary, 1 tablespoon at a time, to prevent scorching. Transfer the onion to a bowl; season with salt and pepper.
Line a baking sheet with parchment paper. On a lightly floured work surface, roll out the puff pastry to an 11-inch square. Using a plate as your guide, cut out four 5-inch rounds. Transfer the rounds to the prepared baking sheet and prick them all over with a fork.
Bake the rounds in the center of the oven for about 8 minutes, until puffed and lightly golden. Using the back of a fork, deflate the rounds and bake for about 4 minutes longer, until the pastry is just set.
Top the pastry rounds with the onion, potato slices, bacon and cheese. Bake for about 10 minutes, until the cheese is melted and the pastry is browned. Transfer the tarts to plates; serve hot or warm.