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1
Line the bottoms and sides of two 5 x 9-inch loaf pans with parchment paper; set aside.
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2
Using a serrated knife, trim all edges of the vanilla sheet cake by 1 inch so it measures 8 x 12 inches.
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3
Slice the cake widthwise, through the top, into 3 vertical pieces, each 4 x 8 inches.
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4
Split each piece in half, slicing horizontally through the crumb.
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5
You should have six 4 x 8-inch layers.
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6
Set aside.
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7
Make the semifreddo: In a large heatproof bowl set over a pan of simmering water, whisk together the egg yolks, 1/2 cup granulated sugar, and 2 tablespoons confectioners sugar until smooth.
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8
Add the wine, 1/2 cup lemon juice, and lemon zest; cook, stirring constantly with a wooden spoon, and scraping across the bottom to prevent the mixture from sticking to the bowl, until the mixture is thick enough to coat the back of the spoon, 6 to 7 minutes.
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9
Remove from heat, and transfer to a large bowl.
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10
Let cool to room temperature (or place the pan in an ice-water bath, stirring occasionally).
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11
When the custard has cooled, combine the cold water, 1/2 cup granulated sugar, and remaining teaspoon lemon juice in a small saucepan.
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12
Bring the mixture to a simmer over medium heat.
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13
Cook until the mixture is slightly thickened and registers 240F on a candy thermometer, about 8 minutes; wash down the sides of the pan with a pastry brush dipped in water to prevent crystals from forming.
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14
Remove from heat, and let the mixture cool 2 to 3 minutes.
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15
Meanwhile, in the bowl of an electric mixer fitted with the whisk attachment, beat the egg whites and remaining tablespoon sugar on medium-high speed until stiff but not until dry peaks form.
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16
With the mixer still running, slowly drizzle the syrup mixture into the egg whites; continue beating until the meringue has cooled slightly and the bowl is cool to the touch.
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17
In another large mixing bowl, whip the cream with the remaining 3 tablespoons confectioners sugar until soft peaks form.
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18
Fold the whipped cream into the cooled lemon mixture; fold in the egg white mixture.
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19
The mixture should be very smooth.
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20
Place the rum in a small bowl.
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21
Fit one of the cake layers in the bottom of each prepared loaf pan.
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22
Using a pastry brush, lightly moisten the top of the cake with rum.
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23
Using an offset spatula, evenly spread 1 1/2 cups lemon filling over each.
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24
Repeat the process, making another layer of cake, rum, and filling; cover each with one of the remaining cake layers.
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25
Place in the freezer at least 5 hours or overnight.
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26
Just before serving, remove the pans from the freezer, and turn the cakes out of the pans; remove the parchment paper.
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27
Slice into pieces.
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28
Preheat the oven to 350F.
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29
Line a 9 x 13-inch baking pan with parchment paper, and set aside.
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30
Sift together the flour, salt, and baking powder in a medium bowl.
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31
In the bowl of an electric mixer fitted with the whisk attachment, beat together the egg yolks and sugar on medium-low speed until light and fluffy.
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32
Beat in the water and vanilla bean scrapings.
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33
Add the dry ingredients in 3 batches, scraping down the sides of the bowl with a rubber spatula as needed, just until the flour mixture is incorporated after each addition.
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34
In another mixing bowl, beat the egg whites until stiff but not until dry peaks form; whisk one-quarter of the egg whites into the batter to lighten.
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35
Fold in the remaining egg whites, and pour the batter into the prepared pan.
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36
Bake until the cake springs back when gently pressed in the center, 15 to 20 minutes.
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37
Transfer to a wire rack to cool completely.
