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1
Preheat the oven to 375F.
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2
Spread the almonds in a single layer on a rimmed baking sheet.
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3
Toast until fragrant and light golden brown, 7 to 9 minutes.
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4
Remove from oven and transfer to a plate to cool completely.
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5
In a food processor, pulse toasted almonds, flour, 1/2 cup sugar, and salt until fine crumbs form.
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6
With the machine running, add the butter and 1 egg, processing until mixture is smooth.
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7
Refrigerate frangipane until chilled, about 30 minutes.
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8
Meanwhile, on a lightly floured work surface, roll out Puff Pastry dough to an 18-by-11-inch rectangle, about 1/8 inch thick.
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9
Wrap in plastic, and freeze until chilled, about 10 minutes.
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10
In a medium skillet, combine the pear, remaining tablespoon sugar, and the lemon juice; cook over medium heat until pear slices are caramelized on both sides, about 4 minutes.
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11
Transfer pears to a plate with a slotted spoon, and refrigerate until chilled, about 10 minutes.
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12
In a small bowl, whisk together the remaining egg with the heavy cream; set egg wash aside.
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13
Transfer the dough to a lightly floured piece of parchment paper.
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14
Using a 9-inch round cake pan as a guide, cut out two 9-inch rounds with a sharp knife; do not remove from the dough.
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15
With a floured 1-inch cookie cutter, cut a hole out of the center of one of the rounds, and discard.
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16
Using a floured 2-inch cookie cutter, cut a circle from the excess dough; set aside.
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17
(This will later be used to decorate the finished Pithiviers.)
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18
Reserve remaining dough for another use.
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19
Place the uncut round and the cutout circle on a parchment-lined baking sheet.
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20
Using a pastry bag fitted with a 1/2-inch plain tip (such as an Ateco #806), pipe the chilled frangipane evenly over the center of the round, leaving a 1 1/2-inch border.
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21
Evenly distribute the pear mixture over the frangipane.
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22
Working quickly, lightly brush egg wash over the dough surrounding the frangipane, leaving a 1/2-inch border around the edge.
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23
Cover with the other round of dough, lining up the edges.
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24
Gently lift to allow air to escape, then smooth any remaining air bubbles with your hands.
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25
Press the edges together firmly to seal, and trim with a sharp paring knife.
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26
With the knife, score the top of the pastry, making curved lines from the hole in the center out toward the edges, to resemble a pinwheel.
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27
Place the filled tart in the freezer until firm, about 20 minutes.
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28
Brush the top of the tart and the cutout circle with egg wash, being careful not to let any drip over cut edges, as it will prevent even puffing.
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29
Bake for 30 minutes (remove cutout after 15 minutes).
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30
Reduce oven temperature to 350F; cover edge of pastry with foil to prevent it from burning.
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31
Bake until center is well browned, about 30 minutes more.
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32
Remove from oven, and slide onto a wire rack to cool.
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33
Serve at room temperature, placing the cutout circle in the center if desired.
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34
A cake pan is used to cut two 9-inch rounds from a large rectangle of dough.
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35
A small piece is cut from one of the rounds, and a larger piece is cut from the excess dough.
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36
The frangipane is piped over one round, then topped with the pear filling.
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37
The tart is trimmed, scored, and brushed with egg wash before baking.
