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To Make the curd
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Combine sugar and cornstarch in a saucepan. Pour in water and the lime juice.
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Over medium heat, stir the mixture constantly until it thickens and comes to a boil.
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Boil for 1 minute. Remove the pan from the heat.
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Spoon about 1/2 cup of the hot mixture into a small bowl containing the egg yolks and stir quickly until combined.
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Pour the egg mixture back into the saucepan. Return pan to medium heat and cook, stirring constantly, for approximately 1 min. The mixture will thicken slightly.
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Remove from heat and stir in the lime zest and the butter until combined.
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Cool completely before using.
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1 8-inch cake
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To make the cake batter
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Preheat the oven to 350°
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Grease and flour three 8 x 2-inch round pans. You can ensure the cake comes out easily by lining the bottom of each pan with a circle of parchment paper before greasing. But that is optional. You can use two pans and slice the cake into four layers. But there will be thinner layers of lime curd.
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In the bowl of a mixer or using a hand mixer, combine the cake flour, sugar, salt, baking powder, and lime zest.
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In a separate bowl, combine eggs, milk, vegetable oil, and lime juice. Blend with a fork.
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Start your mixer on low speed and add a few pats of butter, gradually increasing to medium speed as you add more slices of butter. Beat until the dry ingredients are crumbly and moistened by the butter. The look & texture will be similar to coarse sand. There can be small pieces of butter, and they will blend in the next step.
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Scrape the bottom and sides of the bowl to make sure there is no dry flour.
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Slowly add approximately 1/2 of the egg mixture to the dry ingredients and beat at medium speed for 1 1/2 minutes. The batter will become thick and fluffy.
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Scrape the bowl and add the remaining egg mixture in 2 additions. Beat for 20 seconds and scrape down the sides of the bowl after each addition.
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Spread into the prepared pans. Give each pan a tap to release any large air pockets.
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Bake at 350 degrees for 25 to 30 minutes (30 to 35 minutes if you bake in two pans) until a toothpick inserted in the center comes out clean.
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Let cakes cool for 10 minutes, then turn out onto a cooling rack.
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To make the frosting
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Combine butter and cream cheese in the bowl of a stand mixer (or you may use a hand mixer) and beat until creamy, well-combined, and lump-free.
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Add the lime juice, zest, and salt and stir well to combine.
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With the mixer on low, gradually add powdered sugar until thoroughly combined.
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To assemble the cake:
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Using a piping bag, pipe a ring of frosting around the edge of the top of the bottom layer of the cake.
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Spread ½ the lime curd onto the top inside the piped ring.
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Place the next layer and repeat with the remaining ½ of the lime curd.
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Place the final layer on top of the filled layers. Frost and decorate as you want.