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1
: Sift flour and set aside. In the bowl of a stand mixer fitted with a paddle attachment, cream the butter and sugar on high speed until light and fluffy, stopping regularly to scrape down the sides, bottom and paddle, about 8 minutes. Add the egg and yolk one at a time, and beat well between additions. Scrape one more time, then give it a good final mix on high speed. Add the coconut, mix one last time on high speed. Stop the mixer. Add the flour, salt, cream and vanilla. Mix on low until the dough comes together, about 30 seconds. Finish mixing by hand with a large rubber spatula. Divide the dough into two flat, round disks about 4-inches across. Double wrap tightly in plastic wrap and chill for at least two hours.
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2
: Dampen the surface of a sheet tray and line the bottom and sides with plastic wrap. Keep the roll of plastic wrap handy, and set aside. In a medium sized bowl, combine the starch and half the sugar and whisk together until incorporated. Add the eggs and yolks and whisk until pale yellow, about 2 minutes without stopping. Set aside. In a medium saucepan, combine half the sugar, milk, and salt and stir. Set over medium heat and bring to a simmer. Temper the egg mixture by adding the hot milk a quarter cup at a time, whisking thoroughly between additions. Pour the liquid back into the pot and whisk over low heat. Continue to whisk as the mixture thickens. Whisk through the lumps until the pastry cream becomes smooth. When it begins to bubble, whisk for two additional minutes, then remove from heat. Whisk in the butter and vanilla extract until they melt and fully incorporate. Scrape the pastry cream onto the prepared sheet and press another layer of plastic over the surface. Allow it to cool to room temperature. Transfer to the fridge to chill for at least two hours.
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3
1 hour before baking, roll out the dough on a heavily floured surface, until it is just shy of 1/4-inch thick. Roll the dough back onto the rolling pin, then gently roll it out over the tart pan. Press the dough into the pan to shape it, then cut off the excess, leaving 1/4-inch of overhang. Chill for one hour.
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4
Adjust oven rack to center position and preheat the oven to 300u00b0F. Line a sheet tray with a silicone baking mat. Brush the pineapple pieces with butter on both sides, and sprinkle them with sugar. Roast in the oven for approximately 40 minutes, turning them frequently, until they caramelize slightly on the edges. Remove from the oven, loosen gently with a spatula to ensure that they won't stick, then allow them to cool.
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5
Adjust oven rack to center position and preheat the oven to 350u00b0F. Remove the tart shell from the fridge, trim the overhang off of the edge of the tart, patch any thin parts or cracks with excess dough. Line the tart shell with foil and fill with weights or beans. Place the tart in the center of the bottom rack of the preheated oven. Bake for 20 minutes, rotating halfway through. Remove the weights and foil, and continue to bake until the bottom is golden brown, about 15-20 additional minutes. Cool the shell completely before removing from the pan or filling.
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6
When you're ready to serve, beat the pastry cream with the paddle attachment of a stand mixer on high speed until it is smooth and creamy. Select the 4 nicest looking pineapple rounds and set aside. Chop the rest of the pineapple rounds into 1/2 inch pieces. Line the bottom of the cooled tart shell with the pieces. Spread the whipped pastry cream over the top, so it leaves a few centimeters of room for the pineapple rounds. Press the rounds into the surface of the tart, so the pastry cream and pineapple are flat across the surface. Sprinkle with sugar all over, brulee the top so the sugar burns and caramelizes. Serve immediately.
