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Preheat oven to 350 degrees F. Generously butter a 9” round cake pan. Line the bottom of the pan with a piece of parchment paper.
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Toast the coconut in a 12” skillet over medium heat. Shake the pan constantly until the coconut is toasted to a light golden colour. Do not leave unattended as coconut burns easily. Immediately transfer the coconut to a plate to cool. Divide coconut evenly into two ½ cup portions. You will need ½ cup for the cake batter and the other ½ cup set aside for the garnish.
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Add the granulated sugar into a small bowl. Zest two limes dropping the zest right into the bowl with the sugar. Stir to combine to infuse the sugar with lime flavour. Set aside while preparing the other ingredients.
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Juice limes to get 4 tablespoons (¼ cup). You will need 2 tablespoons for the cake batter and the other 2 tablespoons set aside for the lime glaze.
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With an electric mixer on medium speed, beat butter and lime infused sugar until fluffy. Beat in eggs one at a time. Beat in 2 tablespoons of the lime juice.
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In a medium bowl stir together flour, baking powder and ½ cup of the toasted coconut.
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At low speed, gradually add flour mixture and coconut milk alternately in batches, beginning and ending with flour, beating in between each addition. Batter will be thick.
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Spoon batter into prepared pan and smooth the top. Bake until golden and a wooden pick inserted comes out clean, about 40 - 45 minutes. Leave cake in pan and let cool slightly, about 1 hour. Turn cake out of pan and place on a serving platter.
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Make the lime glaze; in a small bowl stir together icing sugar and reserved 2 tablespoons lime juice until smooth. Spoon half of the glaze over top of cake, allowing some to drip over the sides. Let the glaze set for 1 - 2 minutes. Spoon remaining glaze over top of cake, allowing more to drip over the sides. Immediately sprinkle the top with reserved ½ cup toasted coconut.
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Garnish cake with lime zest and lime slices as desired.
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If making ahead, cover cake with a dome and refrigerate. Bring cake to room temperature (for about 1 hour or more) before serving.