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Special equipment: a kitchen blowtorch
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For the cake batter: Preheat the oven to 350 degrees F; line cupcake pans with 24 cupcake liners.
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Put the butter in the bowl of a stand mixer with a paddle attachment and beat slowly until it is smooth and creamy.
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Add the granulated sugar and salt and cream at moderate speed until the mixture is light and fluffy, 8 to 10 minutes.
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Add the eggs and egg whites together a little at a time, beating after each addition until the eggs are absorbed before adding more.
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Mix until light and fluffy, scraping down the sides of the bowl to insure even mixing, about 5 minutes.
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Sift together the cake flour and baking powder in a medium bowl and set aside.
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Mix the milk and vanilla together in a separate bowl.
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Add one-quarter of the flour mixture to the butter and egg mixture and beat just until blended in.
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Add one-third of the milk mixture and beat just until blended in.
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Repeat with the remaining ingredients, alternating the flour with the milk, until all the ingredients are used.
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Scrape down the sides of the bowl occasionally for even mixing.
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Scoop some batter into each liner and bake until an inserted toothpick comes out clean, 20 to 22 minutes.
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Let cool completely before frosting.
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For the custard frosting: Using an electric mixer with a whip attachment, whip the cornstarch and egg yolks in a stainless steel bowl until light and fluffy.
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Warm the whipping cream and confectioners' sugar in a saucepan over medium heat.
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When the cream mixture reaches about 100 degrees F, add about half of it to the egg yolks, whisking, and then transfer the mixture back to the saucepan.
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Continue cooking the yolk and cream mixture until it reaches a boil (about 180 degrees F).
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Remove from the heat immediately and pour into a clean stainless steel bowl.
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Whip in the butter and vanilla until smooth and creamy.
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(The mixture may be stored in an air-tight container up to 5 days.)
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For the brulee sugar mixture: Mix together the brown sugar and granulated sugar in a medium bowl.
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Top each cupcake with 1 1/2 ounces of the custard frosting.
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Sprinkle on some of the brulee sugar mixture and torch.
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Repeat several times to desired thickness.