Preheat the oven to 375°. Butter a 9-inch springform pan. Line the bottom of the pan with parchment paper and butter the paper. Dust the pan with flour, tapping out the excess.
In a large bowl, using a handheld electric mixer, whip the egg whites at high speed until soft peaks form.
In a small bowl, whisk the all-purpose flour with the almond flour and salt. In another large bowl, beat the butter and sugar until fluffy. Add the yolks, one at a time, and beat until fluffy. Beat in the chocolate, then beat in the flours. Beat in one-fourth of the whites, then, using a spatula, fold in the rest of the whites until no streaks remain.
Scrape the batter into the prepared pan and smooth the top. Bake the cake in the center of the oven for 35 to 40 minutes, until a toothpick inserted in the center comes out with a few moist crumbs attached. Let the cake cool on a wire rack for 30 minutes, then remove the ring and let the cake cool completely. Invert the cake onto a plate and peel off the parchment. Turn the cake right side up. Using a long serrated knife, cut the cake horizontally into 3 even layers.
In a small microwave-safe bowl, whisk 1/4 cup plus 2 tablespoons of the apricot preserves with 1/4 cup of water and microwave until melted.
Set the bottom of the springform pan on a wire rack and set the rack on a baking sheet. Arrange the top cake layer, cut side up, on the springform pan. Brush the cake with one-third of the melted apricot preserves. Spread 1/2 cup of the unmelted apricot preserves on top and cover with the middle cake layer. Brush the surface with another third of the melted preserves and spread another 1/2 cup of the unmelted preserves on top. Brush the cut side of the final layer with the remaining melted preserves and set it cut side down on the cake. Using a serrated knife, trim the cake edges if necessary to even them out.
In the microwave-safe bowl, microwave the remaining 1/4 cup plus 2 tablespoons of the apricot preserves until melted, about 30 seconds. Press the preserves through a strainer to remove the solids. Brush the preserves all over the cake until completely coated. Refrigerate for 20 minutes until set.
Meanwhile, in a medium saucepan, whisk the corn syrup with the rum and 2 tablespoons of water and bring to a boil. Cook until slightly thickened, about 1 minute. Put the chocolate into a heatproof bowl and pour the hot mixture on top. Let stand until melted, then whisk until smooth. If the chocolate glaze is too thick to pour, whisk in another tablespoon of hot water. Let cool to warm.
Using an offset spatula, scrape off any excess preserves from the cake so that it is lightly coated. Slowly pour half of the warm chocolate glaze in the center of the cake, allowing it to gently coat the top and spread down the side. Spread the glaze to evenly coat the torte. Microwave the remaining glaze for a few seconds and repeat pouring and spreading. Scrape up any excess glaze. Refrigerate for at least 10 minutes to set the glaze, then cut the torte into wedges and serve with the whipped cream.