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1
Bring milk just to a boil in a small heavy saucepan.
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2
Remove from heat and stir in coconut.
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3
Cover and let stand 30 minutes.
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4
Puree in a blender.
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5
Preheat oven to 350F.
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6
Butter 2 (9- by 2-inch) round cake pans and dust with flour, knocking out excess.
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7
Sift together flour, baking powder, and salt.
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8
Beat together butter and sugar in a large bowl with an electric mixer until light and fluffy.
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9
Beat in whites, vanilla, and almond extract until light and fluffy again, about 2 minutes.
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10
Add half of flour mixture and beat on low speed just until blended.
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11
Beat in coconut-milk mixture, then remaining flour mixture, just until blended.
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12
Divide batter evenly between cake pans.
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13
Bake in middle of oven until golden and a tester comes out clean, about 30 minutes.
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14
Cool layers in pans on racks 5 minutes.
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15
Run a thin knife around edges of pans, then invert layers onto racks to cool completely.
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16
Heat whites, sugar, water, corn syrup, and cream of tartar in a large metal bowl set over a saucepan of simmering water, whisking, until mixture is warm and sugar is dissolved.
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17
Beat mixture, still over heat, with a handheld electric mixer on high speed until thick and fluffy, about 7 minutes.
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18
(Depending on mixer and weather, this may take longer.)
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19
Remove frosting from heat.
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20
Add vanilla and beat until cool and spreadable.
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21
Brush any loose crumbs from layers and put 1 layer upside down on a serving plate.
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22
Spread with about 1 1/4 cups of frosting and sprinkle with cup coconut.
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23
Place other layer on top, right side up.
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24
Frost top and sides of cake (you may have some frosting left over) and sprinkle with remaining coconut.
