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1
In a small bowl, mix the egg yolk with the water.
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2
In a food processor, pulse the flour with the sugar, salt and cinnamon.
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3
Add the butter and pulse until the mixture resembles small peas.
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4
Sprinkle on the egg yolk mixture and pulse just until the pastry comes together.
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5
Turn the pastry out onto a sheet of plastic wrap and pat it into a disk.
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6
Wrap and chill until firm, at least 1 hour or overnight.
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7
Preheat the oven to 375.
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8
In a medium saucepan, boil the cider with the dessert wine over moderately high heat until reduced to 1 1/4 cups, about 40 minutes.
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9
Remove from the heat.
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10
Add the brown sugar and corn syrup and season lightly with a pinch of salt and pepper.
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11
In a large bowl, toss the apples with the cornstarch; pour the hot cider syrup over and toss.
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12
Using a slotted spoon, transfer the apples into eight 1-cup ramekins.
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13
Pour the cider syrup from the bowl over the apples and top each mound with 1 piece of butter.
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14
Set the ramekins on a baking sheet and bake for about 45 minutes, stirring the apples occasionally, until browned in spots and just tender.
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15
Cover the ramekins with foil and bake for 10 to 15 minutes longer, until the apples are very tender.
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16
Meanwhile, line a rimmed baking sheet with parchment paper.
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17
On a lightly floured work surface, roll out the pastry 1/4 inch thick.
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18
Using a 4 1/2-inch round cutter, stamp out 8 rounds; if necessary, press the scraps together to stamp out more rounds.
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19
Transfer the rounds to the prepared baking sheet and prick them several times with a fork.
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20
Crimp the edges decoratively and chill until firm, about 10 minutes.
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21
Bake the pastry rounds for about 15 minutes, or until golden and crisp.
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22
Let cool on the baking sheet.
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23
Top each ramekin with a pastry round and bake for 5 minutes longer.
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24
Transfer the ramekins to plates and serve.
