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1
Preheat the oven to 350F (175C).
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2
Coat a 10-cup (2.5-liter) Bundt cake or tube pan with butter or nonstick cooking spray, dust it with flour, and tap out any excess.
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3
To make the cake, into a medium bowl, sift together the flour, baking powder, baking soda, 3/4 teaspoon salt, and the nutmeg.
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4
In a stand mixer fitted with the paddle attachment (or in a bowl by hand), beat together the 1 cup (8 ounces/225 g) butter and 2 cups (400 g) granulated sugar on medium speed until light and fluffy, 3 to 5 minutes.
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5
In a small bowl, beat together the eggs, egg yolks, and vanilla.
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6
With the mixer running, slowly dribble the egg mixture into the butter mixture, stopping the mixer and scraping down the sides of the bowl as needed, until the eggs are completely incorporated.
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7
(The mixture may look curdled, which is normal.)
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8
Gently stir in one-third of the flour mixture, then about half of the 3/4 cup (180 ml) coconut milk.
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9
Mix in about half of the remaining flour mixture, followed by the remaining coconut milk.
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10
Finally, gently stir in the remaining flour mixture just until combined.
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11
Scrape the batter into the prepared pan and bake until the cakes feels just set in the center, 55 to 60 minutes.
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12
While the cake is baking, make the coconut-rum syrup.
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13
In a medium saucepan, warm the 3/4 cup (180 ml) coconut milk and the 6 tablespoons (75 g) granulated sugar, stirring until the sugar dissolves.
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14
Remove from the heat and add the 1/2 cup (125 ml) rum.
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15
When the cake comes out of the oven, leave it in the pan and poke it with a wooden skewer about 60 times.
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16
Spoon about two-thirds of the coconut-rum syrup over the cake, letting it soak in gradually.
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17
Let the cake cool completely.
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18
Invert the cake onto a cake plate.
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19
Brush or spoon the remaining coconut-rum syrup over the cake.
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20
To make the glaze, in a small saucepan over high heat, bring the 4 tablespoons (2 ounces/60 g) butter, the cream, brown sugar, and pinch of salt to a boil.
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21
Cook, stirring to dissolve the sugar, for 1 1/2 minutes.
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22
Remove from the heat, stir in the 1 tablespoon rum, and let cool completely.
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23
Once cool, stir in the toasted coconut.
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24
Spoon the glaze over the top of the cake, encouraging it to run down the sides of the cake (if the glaze seems too thick, rewarm it slightly).
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25
The cake can be stored at room temperature for up to 4 days, preferably under a cake dome.
