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1
Very generously butter six 5-inch round metal pie plates; set aside.
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2
On a lightly floured work surface, roll out Puff Pastry to a scant 1/4-inch thickness.
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3
Using a cutter or a small plate as a guide, cut dough into 4 1/2-inch rounds.
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4
Prick rounds all over with a fork.
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5
Transfer to a parchment-lined baking sheet, and chill until firm, about 30 minutes.
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6
Meanwhile, preheat the oven to 425F.
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7
Lay two or three onion rounds on the bottom of each pie pan.
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8
Using a mandoline or sharp knife, slice the potatoes into thin rounds, about a scant 1/4 inch thick.
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9
Place the potato slices, slightly overlapping, over the onion in two layers of concentric circles (they should completely cover the onion).
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10
Sprinkle potatoes generously with salt and pepper.
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11
Place chilled Puff Pastry rounds on top of the potatoes in each pie plate.
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12
Bake until golden brown, about 20 minutes.
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13
Immediately invert the tartlets onto a platter.
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14
In a small saucepan, combine the balsamic vinegar and sugar.
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15
Bring to a simmer and cook until the mixture reduces to a syrup, about 4 minutes.Whisk in the butter, a piece at a time, until incorporated.
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16
Season with salt and pepper.
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17
Glaze the tartlets with the balsamic syrup and serve warm.
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18
Thinly sliced layers of onions and potatoes are topped with rounds of puff pastry before baking.
