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1
In a large bowl, whisk the flour with the sugar and salt.
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2
Using a pastry blender, cut in the butter until the mixture resembles coarse meal.
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3
In a small bowl, whisk the egg with the egg yolk, then whisk in the water.
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4
Drizzle the egg over the flour mixture, and stir with a fork to lightly blend the ingredients.
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5
Squeeze gently until a smooth dough forms.
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6
Divide it in half, pat each half into a disk and wrap in plastic.
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7
Refrigerate until firm, about 1 hour.
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8
Preheat the oven to 350.
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9
On a floured work surface, roll 1 of the pastry disks into a rough 9-by-24-inch rectangle about 1/8 inch thick.
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10
Using a plate as a guide, cut out three 8-inch rounds.
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11
Transfer them to a large baking sheet with plastic wrap between them to prevent sticking.
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12
Repeat with the remaining pastry disk.
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13
Cut out leaf decorations from the scraps to use for garnish.
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14
Refrigerate the rounds and decorations until firm, at least 20 minutes.
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15
Remove from the refrigerator and let stand until pliable, about 2 minutes.
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16
Lightly oil a large rimmed baking sheet.
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17
Drape a pastry round over each apple and wrap the apples without stretching the pastry, tucking it around and underneath to form a neat package.
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18
Transfer the apples to the baking sheet.
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19
Using a small knife, make a hole in the pastry at the top of each apple and press the cinnamon sticks on the diagonal through the holes and into the apples, creating stems.
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20
Brush the pastry with the beaten egg and bake the apples for about 1 hour, or until they are cooked through and the pastry is nicely browned.
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21
In a large skillet, sprinkle the plums with the sugar and bring to a simmer over moderately high heat.
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22
Stir well, cover and simmer over moderate heat, stirring occasionally, until just tender, about 8 minutes.
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23
Using a slotted spoon, transfer the plums to a large heatproof bowl.
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24
Add the Armagnac to the skillet and simmer over moderately high heat until the cooking liquid is syrupy, about 3 minutes.
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25
Add the syrup to the plums.
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26
Let the apples cool on the baking sheet for about 5 minutes.
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27
Using a metal spatula, transfer the apples to plates.
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28
Serve with the plum sauce.
