Key Lime Meringue Cake

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.

Sift flour, baking powder, and salt together into a bowl.

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.

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.

Cool for 15 minutes in pans on racks. Run a thin knife around sides of pans, invert cake layers onto racks, and cool completely.

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.

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.

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.

•Limes, whether Key or Persian, can vary tremendously in the amount of juice they hold; some can be quite dry and pulpy inside, while others will release plenty of liquid. That makes it difficult to give you, the cook, an idea of how many limes you'll need. We think you'll be safe buying a total of 1 1/2 pounds Key limes or 10 medium Persian limes to make the cake layers, filling, and icing. But don't be surprised if you have extra. Use them up in a batch of margaritas!•Cake layers (not split) can be made 1 day ahead and chilled, wrapped individually in plastic, or frozen 1 week. Halve chilled layers while still cold, but defrost frozen layers before attempting to halve them. Filling can be refrigerated, covered, overnight. Stir before using.•The egg whites in the frosting are not cooked. If this is a concern, you can substitute reconstituted dried egg whites, such as Just Whites. Cake can be assembled and frosted 2 hours ahead if using fresh whites, and 6 hours ahead if using dried whites. Alternatively, cake can be filled but not frosted 1 day ahead. Wrap well in plastic and chill.

Let stand at room temperature 1 hour before frosting it.