Preheat the oven to 350 degrees. Butter and flour a stainless-steel bowl that is 10 inches across and 4 1/2 inches deep; set aside. In a medium mixing bowl, sift together flour and baking powder; set aside.
In the bowl of an electric mixer fitted with the paddle attachment, combine butter and 2 cups sugar. Split the vanilla beans lengthwise, and scrape the seeds into the bowl with the butter and sugar, reserving pods for another use. Beat on medium speed until light and fluffy, about 3 minutes. With the mixer on low speed, add the dry ingredients, alternating with milk, starting and ending with dry ingredients; scrape down sides twice.
In the clean bowl of electric mixer fitted with the whisk attachment, beat egg whites on high with salt until soft peaks form. Add the remaining 1 tablespoon sugar, and continue to beat until stiff glossy peaks form, 3 to 5 minutes. Whisk one-third of the beaten whites into the batter to lighten the mixture. Gently, but thoroughly, fold in remaining whites.
Pour batter into prepared bowl. Bake until golden brown and a cake tester inserted into the center comes clean, 1 hour and 30 minutes to 1 hour and 40 minutes. Remove to a rack to cool for 5 minutes. Invert onto the wire rack to cool completely.
Place cake on work surface flat-side down. Using a serrated knife, cut cake horizontally into 4 layers. The cake will be assembled in layers of decreasing size. Place the first (largest) layer on a cardboard cake round. Brush with simple syrup. Coat with a 1/4-inch-thick layer, about 1 cup, buttercream. Top with second layer. Brush with simple syrup. Spread apricot jam in an even layer over cake. Top with third layer. Brush with simple syrup. Coat with a 1/4-inch-thick layer, about 1/2 cup, buttercream. Top with remaining layer of cake. Brush the assembled cake with simple syrup. Lightly coat cake with a thin layer, about 1/2 cup, buttercream.
Pipe meringue onto cake with a medium-large star tip (.375-inch) to completely cover, pulling up as you pipe to form points. Using a small kitchen torch, lightly brown the meringue all over. Let cake stand at room temperature until ready to serve, up to 6 hours.
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