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1
Preheat the oven to 425u00b0F degrees.
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2
Line a sheet pan with parchment paper.
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3
Heat 3 tablespoons of olive oil in a large skillet over medium-low heat and add the onions and garlic; saute for 15 to 20 minutes, stirring frequently, until the onions are limp and there is almost no moisture remaining in the skillet.
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4
Add 1/2 teaspoon salt, 1/4 teaspoon pepper, the wine and thyme and continue to cook for another 10 minutes, until the onions are lightly golden.
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5
Unfold each sheet of puff pastry on a lightly floured surface and roll it lightly to an 11-by-11-inch square.
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6
Using a six-inch-wide saucer or other circular object as a guide, cut 2 (six-inch) circles from each sheet of puff pastry, discarding the scraps.
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7
Repeat with the second sheet of pastry.
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8
Using the tip of a sharp paring knife, score a circle 1/2 inch inside the edge of each pastry. Prick the pastries all over with the tines of a fork and place them on the sheet pan.
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9
Sprinkle a tablespoon of the grated Parmesan on each round, staying inside the scored border.
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10
Place 1/4 of the onion mixture on each circle, again staying within the scored edges.
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11
Crumble 1 ounce of goat cheese on top of the onions.
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12
Place a slice of tomato in the center of each tart.
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13
Brush the tomato lightly with olive oil and sprinkle with basil, salt, and pepper.
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14
Finally, scatter 4 or 5 shards of Parmesan on each tart.
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15
If the pastry is warm, chill for 15 minutes.
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16
Bake for 20 to 25 minutes, until the pastry is golden brown.
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17
Garnish each with a sprig of thyme and a drizzle of olive oil.
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18
Serve warm.
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19
Enjoy!