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Cupcakes: Preheat oven to 350. Line 12 muffin cups with paper liners. In a bowl, sift together flour, baking powder and salt. In another bowl, using mixer on medium-high speed, beat together the sugar and butter until the mixture is light in texture, 2 to 3 minutes. Beat in the egg yolks, one at a time, then beat in the vanilla. Reduce the speed to low and the flour mixture in 3 additions alternately with the coconut milk in 2 additions, beginning and ending with the flour mixture and scraping down the bowl as needed, beating just until smooth.
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In another bowl, using the mixer on high speed, beat the egg whites until soft peaks form. Stir one-fourth of the whites into the batter to lighten it, then fold in the remaining whites, leaving some whites visible. Gently fold in the coconut flakes. Divide the batter evenly among the lined muffin cups, filling them about three-fourths full. Bake until a toothpick inserted in the center comes out clean, about 20 minutes. Let cool for 5 minutes in the pan, then turn out onto a wire rack and let cool completely. Leave the oven on.
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Frosting: Spread the coconut flakes on a rimmed baking sheet. Bake, stirring occasionally, until lightly toasted, about 10 minutes. Let cool completely. In a bowl, using the mixture on low speed, beat together the cream cheese, butter, lemon juice and vanilla. Gradually beat in the confectioners sugar until the icing is smooth. Spread the frosting on the cool cupcakes, dividing it equally. Sprinkle with the toasted coconut, then serve.
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Variation: For coconut layer cake, divide the batter between 2 buttered and floured 8-inch round cake pans. Bake until the cakes begin to pull away from the sides of the pans, about 25 minutes. Make a double batch of the frosting. Assemble the cake and garnish with 1 cup toasted dried coconut flakes.
