1 cup plus 2 tablespoons unbleached all-purpose flour
1/4 cup plus 1 tablespoon Dutch-process cocoa powder, divided
6 large eggs, separated
1/4 teaspoon kosher salt
1 teaspoon pure vanilla extract
3/4 cup granulated sugar
1 tablespoon confectioners’ sugar
1/3 cup dark rum
1/3 cup granulated sugar
1 cup heavy cream
1/4 cup confectioners’ sugar
Milk chocolate shavings, for decorating
Filling: Place chocolate in a medium heatproof bowl. In a small bowl, sprinkle gelatin over 2 tablespoons milk; let stand until softened, about 5 minutes. In another medium bowl, whisk together egg yolks and granulated sugar.
Bring 1/4 cup cream and remaining 1/4 cup milk to a simmer in a medium saucepan over medium heat. Add one-third of cream mixture to yolk mixture, whisking constantly. Add remaining cream mixture in a slow, steady stream, whisking constantly; return to saucepan. Cook over medium heat, whisking constantly, until custard coats the back of a spoon, about 3 minutes. Remove from heat and stir in gelatin mixture. Strain mixture through a fine-mesh sieve into bowl with chocolate; let stand until softened, 1 minute. Stir until smooth. Cover with plastic wrap, pressing it directly onto surface to prevent skin from forming; let cool completely.
Whisk remaining 3/4 cup cream to soft peaks and gently fold into custard. Refrigerate until ready to assemble, up to 1 day.
Ladyfingers and Cake Layers: Preheat oven to 350 degrees. Using a pencil and ruler, make a template that will be the guide for piping ladyfingers and cake layers: On a piece of parchment, draw two sets of parallel lines spaced 3 1/2 inches apart. On a second piece of parchment, trace three 5-inch circles. Place each piece of parchment, pencil-side down, on an unrimmed baking sheet. Sift together flour and 1/4 cup cocoa into a medium bowl.
In the bowl of a mixer fitted with the whisk attachment, beat together egg whites, salt, and vanilla on medium speed until frothy. Increase speed to high and gradually add 1/2 cup granulated sugar, beating until stiff, glossy peaks form, about 3 to 5 minutes. In a separate bowl fitted with the whisk attachment, beat egg yolks with remaining 1/4 cup granulated sugar until thick and pale yellow, about 2 minutes. Gently fold egg-yolk mixture into egg-white mixture, then fold in flour mixture in three additions. Transfer to a piping bag fitted with a 1/2-inch round tip.
Pipe ladyfingers crosswise onto prepared templates, spacing 1/4 inch apart (you’ll need about 16), then pipe cake rounds, starting in center of each circle and spiraling outward until you reach edge of template. Whisk together remaining 1 tablespoon cocoa and confectioners’ sugar; sift over cake rounds. Bake ladyfingers and cake rounds until firm and springy, about 14 minutes. Transfer sheets to wire racks; let cool completely.
Assembly: Place a 6-by-3-inch cake ring on a parchment-lined baking sheet; line ring with a 20-by-3-inch parchment strip to form a collar. Bring rum and granulated sugar just to a boil in a small saucepan, stirring until sugar is dissolved; remove from heat. Place ladyfingers standing upright inside of ring, with domed sides facing out (use just enough to fit snugly). Place one cake layer at bottom of ring. Brush ladyfingers and cake with rum syrup. Pour half of chocolate filling into cake ring and top with a second cake layer. Brush cake with syrup and top with remaining chocolate filling. Top with final cake layer and brush with syrup. Refrigerate until firm, at least 4 hours or overnight.
Just before serving, whisk cream and confectioners’ sugar to soft peaks. Carefully remove charlotte from bottom piece of parchment and transfer, still in cake ring, to serving platter. Remove ring and gently peel off parchment strip. Dollop whipped cream on top of cake and sprinkle with chocolate shavings.
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