Individual Potato-and-Onion Tartes Tatin

Very generously butter six 5-inch round metal pie plates; set aside. On a lightly floured work surface, roll out puff pastry to a scant 1/4-inch thickness. Using a cutter or a small plate as a guide, cut dough into 4 1/2-inch rounds. Prick rounds all over with a fork. Transfer to a parchment-lined baking sheet; chill until firm, about 30 minutes. Meanwhile, preheat oven to 425 degrees.

Lay two or three onion rounds on the bottom of each pie pan. Using a mandoline or sharp knife, slice potatoes into thin rounds, about a scant 1/4 inch thick. Place potato slices, slightly overlapping, over the onion in two layers of concentric circles (they should completely cover the onion). Sprinkle potatoes generously with salt and pepper. Place chilled puff pastry rounds on top of the potatoes in each pie plate. Bake until golden brown, about 20 minutes.

Immediately invert tartlets onto a platter. In a small saucepan, combine balsamic vinegar and sugar. Bring to a simmer and cook until mixture reduces to a syrup, about 4 minutes. Whisk in butter, a piece at a time, until incorporated. Season with salt and pepper. Glaze tartlets with balsamic syrup and serve warm.