• 3/4 cup (11/2 sticks) unsalted butter, room temperature, plus more for pans
• 2 1/2 cups (spooned and leveled) all-purpose flour, plus more for pans
• 1 tablespoon baking powder
• 1 teaspoon salt
• 1 1/2 cups sugar
• 2 large eggs plus 3 large egg yolks (reserve whites for frosting)
• 1 teaspoon vanilla extract
• 1 cup whole milk
• Seven-Minute Frosting (below)
• 1/4 cup lemon curd and 1 1/4 Cups sweetened shredded coconut, for assembling
  
• Seven-Minute Frosting
  
• 3 large egg whites
• 2 teaspoons light corn syrup
• 1/2 teaspoon cream of tartar
• 1/3 cup cold water
• 1 1/2 cups sugar

Lemon curd, made from lemon juice, sugar, egg yolks, and butter, adds tartness to the filling. Look for jars of curd next to jams and jellies in the supermarket.

1. Preheat oven to 350 degrees, with rack in center. Butter two 9-inch round cake pans. Line bottom of pans with parchment-paper rounds; butter paper. Dust paper and sides of pans with flour, tapping out excess.
2. In a large bowl, whisk together flour, baking powder, and salt; set aside. With an electric mixer, cream butter and sugar until light and fluffy. Add eggs and yolks, one at a time, beating well after each addition. Beat in vanilla. Add flour mixture in three additions, alternately with milk in two, beginning and ending with flour.Mix until just combined.
3. Divide evenly between prepared pans. Place pans next to each other in oven (without touching); cook until a toothpick inserted in centers comes out clean, about 30 minutes, rotating pans halfway through.
4. Cool in pans 10 minutes. Run a knife around edges; invert cakes onto a rack. Peel off parchment; reinvert and let cool completely before assembling.
5. Assemble the cake: In a small bowl, whisk 1/4 cup store-bought lemon curd with 3/4 cup Seven-Minute Frosting. Place bottom cake layer on a platter; tuck strips of parchment under edges of cake.
6. Leaving a 1-inch border, spread layer with lemon-curd mixture and 1/2 cup sweetened shredded coconut. Top with remaining cake layer.
7. Spread 2 cups frosting over top; spread remaining on sides (push spatula in a forward motion to prevent crumbs). Sprinkle 1 1/4 cups coconut over cake; pat gently on sides.

Seven-Minute Frosting

1. In a medium saucepan, bring 2 inches of water to a simmer.
2. In a large heatproof mixing bowl, combine reserved egg whites, light corn syrup, cream of tartar, water, and sugar.
3. Place bowl over simmering water (it should not touch water); with a handheld mixer, beat on high speed until stiff peaks form, about 7 minutes.
4. Remove bowl from heat; beat 3 to 5 minutes more to cool. Use immediately.