Special equipment: six 6-inch pie tins
For the pie crust: Pulse the flour, confectioners' sugar and salt in a food processor. Add the butter and pulse until a coarse meal forms. Drizzle in the yolk and pulse until the mixture reaches a cornmeal-like consistency. Remove from the processor and gently divide the dough among six 6-inch pie tins. Gently press the dough into the tins and up against the edges. Poke the bottom of the crusts a few times with a fork. Butter 6 squares of aluminum foil (large enough to cover the pie crusts) and press one, butter-side down, into each crust. Freeze until hard, 20 to 30 minutes.
Preheat the oven to 425 degrees F.
Spread the coconut on a baking sheet and toast in the oven, tossing once, until toasted, about 3 1/2 minutes.
Bake the pie crusts in the oven until the edges are golden, about 15 minutes. Allow to cool and then carefully remove and discard the foil. Set the pie crusts aside until ready to fill.
For the coconut pastry cream: Bring the coconut milk and cream of coconut to a simmer in a medium saucepan.
Add the sugar and cornstarch to the bowl of a stand mixer with a whisk attachment. Whisk until combined, then add the egg and yolks and whisk on high speed until the mixture reaches a pale yellow color and it drops down like ribbons when you lift the whisk.
Add a couple of ladlefuls of the hot coconut milk mixture to the egg mixture and whisk to temper the eggs, then pour all of the egg mixture into the coconut milk saucepan and return to medium heat. Whisk vigorously and constantly until the custard starts to boil and thicken.
Place a bowl over an ice bath and strain the pastry cream into the bowl to remove any lumps. Place a layer of plastic wrap on the surface of the pastry cream to prevent a skin from forming. Refrigerate over the ice bath until cool and firm, 15 to 20 minutes.
Whip the heavy cream in a medium bowl until it reaches stiff peaks, refrigerate until ready to use.
For the salted lime caramel: Add the sugar to a medium saucepan. Pour 1/4 cup of water and squeeze the lime juice over the sugar, swirling the pan to fully moisten. Cook over medium-heat until bubbling and deep amber in color, 15 to 20 minutes. Turn off the heat, carefully whisk in the cream. Whisk in the butter piece by piece. Finish with a sprinkling of fleur de sel.
For the candied key lime slices: Preheat the oven to 250 degrees F. Line a baking sheet with a silicone mat. Make a simple syrup: Heat the sugar and 1 cup of water in a small saucepan until the sugar is dissolved. Remove from the heat and let cool.
Slice the key limes into 1/16-inch slices with a mandolin. Brush the slices with the simple syrup and place in a single layer on the prepared baking sheet making sure they do not overlap. Bake for 30 minutes. Allow to cool before using.
For serving: Whisk the coconut custard until it is light and smooth. Gently fold in the whipped cream. Spoon the mixture into the pie crusts. Top with the toasted coconut flakes. Place a spoonful of the salted lime caramel on each plate and place a pie on it. Drizzle with more salted lime caramel and garnish with a candied key lime slice.
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