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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.
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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.
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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.
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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.
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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.
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Leaving a 1-inch border, spread layer with lemon-curd mixture and 1/2 cup sweetened shredded coconut. Top with remaining cake layer.
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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.