This vanilla sheet cake is topped with lemony semifreddo ("half-frozen" in Italian)—a rich chilled mousse.
Line bottoms and sides of two 5-by-9-inch loaf pans with parchment paper; set aside. Using a serrated knife, trim all edges of vanilla sheet cake by 1 inch so it measures 8 by 12 inches. Slice cake widthwise, through the top, into three vertical pieces, each 4 by 8 inches. Split each piece in half, slicing horizontally through the crumb. You should have six 4-by-8-inch layers. Set aside.
Make the semifreddo: In a large heatproof bowl set over a pan of simmering water, whisk together egg yolks, 1/2 cup granulated sugar, and 2 tablespoons confectioners' sugar until smooth.
Add wine, 1/2 cup lemon juice, and lemon zest; cook, stirring constantly with a wooden spoon, and scraping across the bottom to prevent mixture from sticking to bowl, until mixture is thick enough to coat the back of the spoon, 6 to 7 minutes. Remove from heat, and transfer to a large bowl. Let cool to room temperature, or place pan in an ice bath, stirring occasionally, to expedite chilling.
When custard has cooled, combine the water, 1/2 cup granulated sugar, and remaining teaspoon lemon juice in a small saucepan. Bring mixture to a simmer over medium heat. Cook until mixture is slightly thickened and registers 240 degrees on a candy thermometer, about 8 minutes; wash down sides of pan with a pastry brush dipped in water to prevent crystals from forming. Remove from heat, and let mixture cool 2 to 3 minutes.
Meanwhile, in the bowl of an electric mixer fitted with the whisk attachment, beat egg whites and remaining tablespoon sugar on medium-high speed until stiff but not dry peaks form. With mixer still running, slowly drizzle syrup mixture into egg whites; continue beating until meringue has cooled slightly and the bowl is cool to the touch.
In another large mixing bowl, whip cream with remaining 3 tablespoons confectioners? sugar until soft peaks form. Fold whipped cream into cooled lemon mixture; fold in egg white mixture. Mixture should be very smooth. Place rum in a small bowl.
Fit one of the cake layers in the bottom of each prepared loaf pan. Using a pastry brush, lightly moisten top of cake with rum. Using an offset spatula, evenly spread 1 1/2 cups lemon filling over each. Repeat process, making another layer of cake, rum, and filling; cover each with one of the remaining cake layers. Place in freezer at least 5 hours or overnight.
Just before serving, remove pans from freezer, and turn cakes out of pans; remove parchment paper. Slice into pieces.
For perfectly smooth slices, cut the layered cake with a hot serrated knife. Cake can be wrapped well in plastic wrap and stored in the freezer for up to three weeks.