Ginger-Lime Coconut Cake with Marshmallow Frosting

PreparationFor ginger-lime curd: Whisk eggs, yolks, sugar, lime juice, lime peel, ginger, and salt in large metal bowl to blend. Place bowl over saucepan of barely simmering water (do not allow bottom of bowl to touch simmering water); whisk constantly until curd thickens, about 8 minutes. Remove bowl from over simmering water; whisk butter into curd. Strain through fine strainer set over bowl; discard solids in strainer. Press plastic wrap directly onto surface of curd; chill overnight. (Curd can be made up to 2 days ahead. Keep refrigerated.) For cake: Position 1 rack in top third and 1 rack in bottom third of oven and preheat oven to 350°F. Butter four 9-inch-diameter cake pans with 1 1/2-inch-high sides. Line bottoms of pans with parchment paper rounds. Butter parchment; dust with flour. Sift flour, baking soda, and salt into large bowl. Using electric mixer, beat butter in another large bowl until smooth. Gradually add sugar and beat until very well blended, about 5 minutes. Beat in eggs 1 at a time, scraping down sides of bowl before each addition. Beat in flour mixture in 3 additions alternately with buttermilk in 2 additions. Divide batter equally among prepared cake pans. Place 2 cake pans on top rack of oven and 2 pans on bottom rack; bake until golden and tester inserted into cake centers comes out clean, reversing pans after 15 minutes, about 30 minutes total. Cool cakes in pans on racks 10 minutes. Turn cakes out onto racks; peel off parchment paper. Turn cakes right side up on racks; cool cakes completely. Place 1 cake layer on platter. Spread 1/3 of ginger-lime curd (about 1/2 cup) over, leaving 1/2-inch plain border around edge of cake. Repeat procedure on 2 more cake layers. Let each cake layer stand 10 minutes. Stack cake layers, curd side up. Top with fourth cake layer. Let cake stand at room temperature while preparing frosting. Insert 3 or 4 bamboo skewers from top to bottom into cake to hold stacked cake layers in place while frosting. For frosting: Whisk sugar, egg whites, 1/3 cup water, light corn syrup, and cream of tartar in large metal bowl to blend. Set bowl over saucepan of barely simmering water (do not allow bottom of bowl to touch simmering water). Using handheld electric mixer, beat on medium speed until mixture resembles soft marshmallow fluff, about 4 minutes. Increase mixer speed to high and beat until mixture is very thick, about 3 minutes longer. Remove bowl from over simmering water. Add vanilla extract and continue beating until marshmallow frosting is completely cool, about 5 minutes longer. Spread marshmallow frosting thinly over top and sides of cake. Remove bamboo skewers. Press flaked coconut into marshmallow frosting on top and sides of cake. (Cake can be prepared 1 day ahead. Cover with cake dome and refrigerate. Let stand at room temperature 2 hours before serving.)