How to Make It
In a small saucepan, bring the half-and-half to a simmer. In a medium bowl, whisk the yolks, sugar, flour, cornstarch and salt. Whisk in the hot half-and-half. Return the mixture to the saucepan and cook over moderate heat, whisking constantly, until very thick, about 3 minutes. Whisk in the butter and vanilla. Scrape the pastry cream onto a large plate and let cool to room temperature, about 10 minutes.
Preheat the oven to 375°. Butter an 8-inch springform pan. In a medium bowl, whisk the pastry cream with the 6 tablespoons of butter until smooth. Whisk in the lemon zest and juice. Add 1/4 cup plus 2 tablespoons of the sugar, the cake flour, semolina, baking powder and salt and whisk the batter until smooth.
In a clean bowl, using an electric mixer, beat the egg whites at medium speed until soft peaks form. Gradually beat in the remaining 1/2 cup of sugar at high speed until the whites are glossy and stiff. At low speed, beat one-fourth of the beaten whites into the batter, then fold in the rest with a rubber spatula until no streaks of white remain.
Scrape the batter into the prepared pan and bake in the lower third of the oven for about 40 minutes, until the cake is golden and a skewer inserted in the center comes out with a few moist crumbs attached. Let cool in the pan for 20 minutes, then remove the ring and base and transfer to a rack to cool completely.
Using a serrated knife, split the cake in half horizontally. Spread the preserves on the bottom layer and replace the top. Dust with confectioners' sugar and serve with raspberries.