INGREDIENTS 

For Cake
1 cup whole milk
1/2 cup grated fresh coconut
2 1/2 cups sifted cake flour (not self-rising; sift before measuring)
1 tablespoon baking powder
1/2 teaspoon salt
1 stick unsalted butter, softened
1 1/2 cups sugar
5 large egg whites
1 teaspoon vanilla extract
1/2 teaspoon almond extract

Lemon curd
1 cup sugar
3/4 cup fresh lemon juice
3 large eggs
3 large egg yolks
1/4 cup (1/2 stick) unsalted butter, cut into 1/2-inch cubes

Syrup
1/2 cup sugar
1/2 cup boiling water
1/4 cup fresh lemon juice

For frosting
3 large egg whites
1 1/2 cups sugar
1/3 cup water
2 teaspoons light corn syrup
1/2 teaspoon cream of tartar
1 teaspoon vanilla
2 1/2 cups grated fresh coconut

DIRECTION 

To Make Cake:
1. 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.

2. Preheat oven to 350°F. Butter 2 (9- by 2-inch) round cake pans and dust with flour, tapping out the excess.

3. 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.

4. 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.

To Make the Simple Syrup:

1. Combine all the ingredients in a nonreactive 2-quart heavy-bottomed saucepan over medium-high heat and bring to a boil. All the sugar should be completely dissolved.

2. Remove from the heat and pour into a clean medium-size bowl. Let cool completely before using or you may cool the syrup over an ice bath. Simple syrup can be stored in the refrigerator, indefinitely, if kept in an airtight container.

To Make Lemon Curd:

1. Cream the butter and sugar with a mixer. Add the eggs and yolks, 1 at a time, and then add the lemon juice slowly and salt. Mix until combined.

2. Pour the mixture into a 2 quart non-reactive saucepan and cook over low heat until thickened (about 10 minutes), stirring constantly. The lemon curd will thicken at about 170 degrees F, or just below simmer. Remove from the heat and cool. (You may need to sieve if there are lumps in the curd.) If not using right away, place in an airtight container and refrigerate.

To Make Frosting:

1. Place the 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. Remove the bowl from heat.

2. Beat the mixture with a handheld electric mixer on high speed until thick and fluffy, about 7 minutes. (Depending on mixer and weather, this may take longer.) Add vanilla and beat until cool and spreadable.

To Assemble Cake:

1. Place 1 cake layer, flat side up, on platter. Brush with 1/4 of syrup. Spread 1/4 cup lemon curd over.

2. Top with second cake layer; brush with 1/4 of syrup and spread with 1/4 cup lemon curd.

3. Repeat with third cake layer, syrup, and lemon curd. Top with fourth cake layer and spread frosting over sides of cake and sprinkle with coconut. Cover cake with cake dome; refrigerate at least 6 hours and up to 1 day.

Notes:
• You may 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. Bring to room temperature before serving.