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1
In the bowl of a food processor fitted with a steel blade, place the flours, sugar and butter.
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2
Pulse 5 or 6 times in 1/2-second bursts to break up the butter.
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3
Add the shortening, turn on the machine and immediately add the ice water, pulsing 2 or 3 times.
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4
The dough should look like a mass of smallish lumps and should just hold together in a mass when a handful is pressed together.
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5
If the mixture is too dry, pulse in more water by droplets.
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6
Turn the dough out onto the work surface and with the heel of your hand, rapidly and roughly push egg-size blobs into a 6-inch smear.
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7
Gather the dough into a relatively smooth cake, wrap in plastic and refrigerate at least 2 hours (or up to 2 days).
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8
Slice the halved apples into 4 lengthwise wedges each, and toss in a large bowl with the lemon juice and zest and 1/2 cup sugar.
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9
Drain the apples after macerating 20 minutes.
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10
In a 9-inch skillet melt the butter over high heat.
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11
Stir in the remaining sugar and cook until the syrup bubbles and caramelizes, and turns a brown color.
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12
Remove the pan from the heat and arrange a layer of apple slices in a neat pattern on the caramel in the skillet, then arrange the remaining apples neatly on top.
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13
Return the pan to moderately high heat and cook for about 25 minutes, covering the pan after 10 minutes.
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14
Every few minutes press down on the apples and baste them with the exuded juices.
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15
When the juices are thick and syrupy, remove the pan from the heat.
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16
On a lightly floured surface, roll the chilled dough into a circle, 3/16-inch thick and 1-inch larger than the top of the pan.
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17
Drape the dough over the apples, pressing the edge of the dough between the apples and the inside of the pan.
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18
Cut 4 small steam holes on the top of the dough.
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19
Bake until the pastry has browned and crisped, about 20 minutes.
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20
Unmold the tart onto a serving dish (so the pastry is on the bottom), and serve warm or cold with whipped cream or vanilla ice cream, as desired.