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Preheat the oven to 350°F. Soak two cake strips, if you have them. Grease and flour (or line with parchment circles and spray with non-stick spray) two 8" square cake pans (or two 9" round cake pans) that are at least 2" deep. Note: If you want a taller cake, use two 8" round cake pans that are at least 2" deep.
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To make the cake: Whisk together the cake flour, coconut milk powder, salt, and baking powder; set aside.
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In a large bowl, beat together the butter and sugar until the mixture is extremely light and fluffy; scrape down the sides and bottom of the mixing bowl after 2 minutes of beating, and beat for at least 3 minutes more. Add 1/4 of the dry ingredients; mix until combined, and scrape the mixing bowl.
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Combine the egg whites, milk, and flavors; add 1/3 of the mixture to the ingredients in the bowl and mix until combined. Continue adding dry and wet ingredients by turns, until all are incorporated. Scrape the sides and bottom of the bowl one last time, and mix for another minute.
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Divide the batter between the two pans, and wrap the outsides with the soaked cake strips. If you don't have cake strips, place the pans in larger pans; add water to the larger pans until it's halfway up the sides of the cake pans. For 9" cakes, bake for 30 to 35 minutes; for 8" cakes, bake for 38 to 42 minutes, until the cake springs back when lightly touched in the center and the edges just begin to pull away from the sides of the pan. A toothpick inserted into the center will come out clean, or with a few moist crumbs clinging to it.
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Remove the cakes from the oven and place on a rack; remove the cake strips. Let the layers cool for 20 minutes, then turn out of the pan and return to the rack to finish cooling completely before filling and frosting.
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To make the frosting: Combine the butter, cream cheese, vanilla, salt, and coconut flavor in a large mixing bowl. Beat the ingredients together at medium speed until smooth, scraping down the sides of the bowl as needed.
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Sift the coconut milk powder and confectioners’ sugar together in a separate large bowl. Gradually add the sugar mixture to the butter and cream cheese mixture, mixing at low speed until fully incorporated then beating at medium-high speed until the frosting is light and fluffy.
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To finish the cake: Split the cooled cake layers horizontally. Place half of one layer on a serving plate; spread with a scant cup of frosting. Place the other cake half on top, spread with another scant cup of frosting. Repeat with the remaining layers until you've used them all. Frost the top and sides of the cake with the remaining frosting.
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To decorate the cake: Press some coconut onto the sides of the cake and sprinkle the remaining over the top.
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Refrigerate the cake until ready to serve, and let it stand at room temperature for an hour before slicing and enjoying.