Ingredients

• 2 3/4 cups sifted cake flour (not self-rising; sift before measuring) plus more for pans
• 2 1/2 teaspoons baking powder
• 1/2 teaspoon salt
• 2 sticks (1 cup) unsalted butter, softened, plus more for pans
• 1 1/2 cups sugar
• 4 large eggs, warmed in shell in a bowl of warm water 5 minutes
• 1 tablespoon grated Key lime or lime zest
• 1 1/2 teaspoons pure vanilla extract
• 1 cup whole milk
• 3/4 cup sugar
• 1/4 cup cornstarch
• Pinch of salt
• 3/4 cup water
• 3/4 cup fresh Key lime or lime juice
• 2 large eggs
• 3 tablespoons unsalted butter, cut into tablespoons
• 2 teaspoons grated Key lime or lime zest
• 2 large egg whites
• 3/4 cup confectioners' sugar
• 2/3 cup light corn syrup
• 2 tablespoons water
• 1 teaspoon pure vanilla extract
• 1 teaspoon fresh Key lime or lime juice
• 1/8 teaspoon salt
• Special equipment: 2 (9- by 2-inch) round cake pans; a powerful handheld electric mixer or a stand mixer

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Instructions

1. Heat oven to 350°F. with rack in middle. Butter cake pans, then line bottoms with rounds of parchment. Dust pans with additional flour, knocking out excess.
2. Sift flour, baking powder, and salt together into a bowl.
3. Beat together butter and sugar in a large bowl with an electric mixer (or a stand mixer fitted with the paddle attachment) at medium-high speed until pale and fluffy, about 3 minutes. Beat in eggs one at a time, beating well after each addition. Beat in zest and vanilla and continue beating until light and fluffy, 3 to 5 minutes more. At low speed, add flour mixture in 3 batches alternately with milk, beginning and ending with the flour mixture and mixing until batter is just smooth.
4. Divide batter between cake pans, spreading it evenly. Bake until a wooden toothpick inserted in the center of each cake comes out clean and cakes begin to pull away from sides of pans, 20 to 25 minutes.
5. Cool for 15 minutes in pans on racks. Run a thin knife around sides of pans, invert cake layers onto racks, and cool completely.
6. For Filling: Whisk together sugar, cornstarch, and salt in a heavy 2-quart saucepan, then whisk in 3/4 cup water and juice until smooth. Whisk together eggs in a medium heat-proof bowl until well combined. Bring juice mixture to a boil over medium heat, stirring with whisk, then reduce heat and continue to cook at a slow boil, stirring with whisk, 1 minute (mixture will be thick). Remove pan from heat. Add half of hot juice mixture to eggs in a slow stream, stirring with whisk. Stir egg mixture into juice in pan and cook over medium-low heat, stirring, just until it reaches a simmer. Remove pan from heat and add butter and zest, stirring until butter is melted. Cover filling with a buttered round of wax paper or parchment paper and chill until cold, about 1 hour.
7. Whisk together sugar, cornstarch, and salt in a heavy 2-quart saucepan, then whisk in 3/4 cup water and juice until smooth. Whisk together eggs in a medium heat-proof bowl until well combined.
8. Bring juice mixture to a boil over medium heat, stirring with whisk, then reduce heat and continue to cook at a slow boil, stirring with whisk, 1 minute (mixture will be thick). Remove pan from heat.
9. Add half of hot juice mixture to eggs in a slow stream, stirring with whisk. Stir egg mixture into juice in pan and cook over medium-low heat, stirring, just until it reaches a simmer. Remove pan from heat and add butter and zest, stirring until butter is melted.
10. Cover filling with a buttered round of wax paper or parchment paper and chill until cold, about 1 hour.
11. For Frosting: Combine frosting ingredients in a large bowl with electric mixer (or stand mixer fitted with the whip attachment). Beat at high speed until frosting is thick and fluffy, 3 to 5 minutes.
12. Combine frosting ingredients in a large bowl with electric mixer (or stand mixer fitted with the whip attachment). Beat at high speed until frosting is thick and fluffy, 3 to 5 minutes.
13. Assemble Cake: Halve each cake horizontally with a long serrated knife. Put 1 layer on a cake stand or a large plate and spread with one-third of filling (about 2/3 cup). Stack remaining cake layers using half of remaining filling between each layer. Spread top and side of cake generously with frosting.
14. Halve each cake horizontally with a long serrated knife. Put 1 layer on a cake stand or a large plate and spread with one-third of filling (about 2/3 cup).
15. Stack remaining cake layers using half of remaining filling between each layer.
16. Spread top and side of cake generously with frosting.