Fresh Coconut Cake

PreparationMake cake layers: Bring milk just to a boil in a small heavy saucepan. Remove from heat and stir in coconut. Cover and let stand 30 minutes. Purée in a blender. Preheat oven to 350°F. Butter 2 (9- by 2-inch) round cake pans and dust with flour, knocking out excess. Sift together flour, baking powder, and salt. Beat together butter and sugar in a large bowl with an electric mixer until light and fluffy. Beat in whites, vanilla, and almond extract until light and fluffy again, about 2 minutes. Add half of flour mixture and beat on low speed just until blended. Beat in coconut-milk mixture, then remaining flour mixture, just until blended. Divide batter evenly between cake pans. Bake in middle of oven until golden and a tester comes out clean, about 30 minutes. Cool layers in pans on racks 5 minutes. Run a thin knife around edges of pans, then invert layers onto racks to cool completely. Make frosting: 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. Beat mixture, still over heat, with a handheld electric mixer on high speed until thick and fluffy, about 7 minutes. (Depending on mixer and weather, this may take longer.) Remove frosting from heat. Add vanilla and beat until cool and spreadable. Assemble cake: Brush any loose crumbs from layers and put 1 layer upside down on a serving plate. Spread with about 1 1/4 cups of frosting and sprinkle with ‚ cup coconut. Place other layer on top, right side up. Frost top and sides of cake (you may have some frosting left over) and sprinkle with remaining coconut. Cooks' notes:•If egg safety is a problem in your area, you may want to use either pasteurized egg whites in the carton or reconstituted powdered egg whites for the frosting. •Cake may be made 1 day ahead and chilled, loosely covered. Bring to room temperature before serving.