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1
To make the cake, position a rack in the lower third of the oven and preheat the oven to 350F.
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2
Grease the sides of the cake pans and line the bottoms with parchment paper.
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3
To toast the coconut, set a plate near the stove.
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4
Spread the coconut in a wide heavy skillet and stir constantly over medium heat until it begins to color slightly.
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5
Turn the heat down (once coconut is hot, it burns easily) and continue to stir until most of the coconut is light golden brown flecked with some white.
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6
(I often take the pan off the heat a little early and continue to stir, letting the residual heat from the pan toast the coconut more slowly and evenly.)
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7
Immediately scrape the coconut onto the plate to stop it from browning, and cool completely before using.
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8
Mix the flour, baking powder, soda, and salt, then sift it three times.
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9
Set aside.
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10
In a small bowl, whisk the eggs together briefly to combine the whites and yolks.
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11
Set aside.
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12
In the bowl of a stand mixer or another large bowl, combine the butter, coconut sugar, 1/3 cup sugar, and vanilla.
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13
Beat on medium speed (or high speed if using a handheld mixer) until light and fluffy, 3 to 4 minutes.
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14
Beat in the eggs a little at a time, taking about 2 minutes to add all of them.
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15
Add one-quarter of the flour mixture and beat on low speed just until no flour is visible.
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16
Stop the mixer and add one-third of the milk.
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Beat just until it is absorbed.
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18
Repeat twice, adding another quarter of the flour and then another third of the milk each time.
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19
Finally add the last of the flour and the toasted coconuts.
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Scrape the bowl as necessary, and beat only enough to incorporate the ingredients after each addition.
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21
Divide the batter evenly between the two pans and spread it level.
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22
Bake until a toothpick inserted into the center comes out clean, 20 to 25 minutes.
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23
Cool the layers in the pans on a rack for about 5 minutes, then unmold and cool completely (right side up) on the rack.
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24
Combine the lime juice, rum, water, and 1 tablespoon of sugar in a small bowl, stirring to dissolve the sugar.
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25
To assemble the cake, place one cake layer on a plate.
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26
Brush it with about one-third of the rum syrup.
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27
To make the filling, whip the cream with the sugar until it just holds a very soft shapeit should seem slightly underwhipped.
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28
Fold in the (untoasted) coconut.
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29
Spread all of the coconut cream over the moistened cake layer.
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30
Brush the least good-looking side of the second cake layer with half of the remaining rum syrup.
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31
Set the cake moist side down on the coconut filling.
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32
Brush the top of the cake with the remaining rum syrup.
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33
Wrap the cake carefully, to keep its shape.
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34
Refrigerate for at least several hours, or overnight, to allow the coconut to absorb moisture from the cream.
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35
To serve, you can simply sift powdered sugar over the cake just before serving, or you can top the cake with caramelized palm or coconut sugar up to 3 hours before serving: If using grated palm sugar, sprinkle it over the top of the cake as evenly as you can.
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36
If using gooier coconut sugar (impossible to sprinkle and too thick to spread), heat it very gently in a small saucepan until it flows like honey, then pour it over onto the top of the cake and spread it with a heated icing spatula.
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37
To caramelize the top, sweep the propane torch all over the sugared surface, always moving it and keeping enough distance to avoid scorching, until the sugar melts, bubbles, and finally turns reddish amber and clear.
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38
If you dont get to reddish amber, the sugar will not harden when it cools.
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39
Before serving, refrigerate the cake for at least 15 minutes to harden the top; or refrigerate for up to several hours, and remove from the refrigerator 30 to 60 minutes before serving.
