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1
Preheat the oven to 375F.
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2
Lightly grease a rimmed baking sheet or line with parchment paper.
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3
Heat the olive oil and butter in a large skillet over medium-high heat until sizzling hot (see Know-how, page 100).
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4
Add the onions, vinegar, sugar, and rosemary and season with salt and pepper to taste.
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5
Reduce the heat to low and cook for about 15 minutes, stirring occasionally, until most of the liquid has evaporated and the onions are caramelized.
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6
Remove from the heat to cool slightly.
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7
While the onions are cooking, flatten the pastry on a lightly floured surface and roll several times, smoothing out the folds, to create a 12-inch square.
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8
Cut into 3-inch rounds using a biscuit or round cookie cutter.
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9
Transfer to the prepared baking sheet and, using a 2 3/4-inch-round cutter, make an indented border on the cut pastry rounds, being careful not to cut all the way through.
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10
Refrigerate for about 30 minutes.
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11
Combine the goat cheese and parsley in a small bowl, stir to soften and combine, and season with salt and pepper to taste.
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12
Bake the pastry rounds for 10 minutes.
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13
Remove from the oven, depress and remove the top layer of the puffed centers with a small knife, and spread a heaping teaspoon of the cheese mixture into the center of each.
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14
Return to the oven and bake for 5 minutes more, until the pastry is golden brown and puffy and the cheese is warm.
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15
Remove from the oven and top each tart with 3 or 4 rings of the caramelized onions.
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16
Serve warm.
