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To make the curd, puree mango, sugar, lime juice and salt in processor or blender.
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Add yolks; puree 15 seconds longer.
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Pour the mixture into a 2 quart saucepan and cook over low heat until thickened (about 10 minutes), stirring constantly.
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The curd will thicken at about 170 degrees F, or just below simmer.
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Whisk in butter 1 piece at a time.
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Remove from heat, carefully transfer to a glass bowl or jar and cover and refrigerate overnight.
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For the Coconut Cake Layers-
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Butter three 8-inch pans or two 9-inch round cake pans. Line with round parchment paper; butter parchment, dust lightly with flour and shake off excess.
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Sift together cake flour, all-purpose flour, baking powder and salt.
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In a separate bowl, combine unsweetened coconut milk and vanilla; whisk to blend, add coconut and stir to blend.
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In a bowl of a stand mixer fitted with a paddle attachment, beat butter and 1½ cups sugar for 3 minutes, or until light and fluffy.
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Add eggs, one at a time, and mix until incorporated; transfer batter to a large bowl.
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Alternately add flour mixture and coconut mixture to batter in 3 batches, until blended.
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In the bowl of a stand mixer fitted with a wire whip, beat egg whites with cream of tartar and 1½ cups sugar to form medium stiff peaks; add to batter, stirring slowly with a balloon whisk until incorporated.
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Spread batter evenly in pans; tap pans on counter to eliminate air bubbles.
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Bake for 30- 35 minutes, or until a toothpick inserted in center comes out clean; cool on cooling racks for 5 minutes. Run a knife around outer edges of pans and invert cakes onto racks.
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To make the Coconut Cream Cheese Frosting, cream cream cheese and butter together until fluffy.
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Turn mixer to low and beat in powdered sugar, add coconut extract.
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Beat on high for 5 minutes.
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To assemble the cake, place cooled cake layer on cake plate.
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Pipe a thick ring of frosting along the edge of the cake, then fill with about ½ cup of mango curd.
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Top with next layer and repeat. Once middle layers have curd, place cake in fridge for 1 hour.
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Once set, frost the outside of the cake and garnish with toasted coconut shavings.