Preheat the oven to 375. Line a 9-by-13-inch rimmed baking sheet with parchment paper. In the bowl of a standing electric mixer fitted with the whisk, beat the egg yolks with 6 tablespoons of the sugar at high speed until the mixture is pale and fluffy, and leaves a ribbon trail when the whisk is lifted, 3 minutes; transfer to a large bowl.
Thoroughly wash and dry the mixer bowl and whisk. Add the egg whites and salt to the bowl and beat at moderately high speed until soft peaks form. Gradually add the remaining 6 tablespoons of sugar and continue beating until the whites are stiff and glossy.
Using a rubber spatula, stir one-fourth of the beaten whites into the yolk mixture, then fold in the remaining whites until no streaks remain. Working in 2 batches, sift the cocoa over the batter and fold gently until fully incorporated. Spread the batter on the prepared baking sheet in an even layer. Bake for 18 to 20 minutes, until the cake feels springy and dry; rotate the pan halfway through baking. Transfer to a rack and let cool completely.
In a small saucepan, combine the water and sugar and bring to a boil over high heat. Reduce the heat to moderate and simmer just until the sugar is completely dissolved, about 1 minute. Remove from the heat and stir in the kirsch.
In a small, microwave-safe bowl, sprinkle the gelatin over the water and let stand until softened. In a small saucepan, combine the milk with the vanilla bean and seeds and bring to a simmer over moderately high heat. Meanwhile, in a medium bowl, whisk the egg yolks with the sugar.
When the milk comes to a simmer, discard the vanilla bean. Slowly whisk the milk into the yolk mixture until thoroughly blended. Transfer the mixture to the saucepan and cook over moderately low heat, stirring constantly, until the custard is thick enough to coat the back of the spoon, about 1 to 2 minutes. Strain the custard into a medium bowl.
Melt the gelatin in the microwave for 15 seconds; stir it into the custard and let cool. Meanwhile, whip the heavy cream until firm. Stir one-fourth of the whipped cream into the custard until incorporated, then fold in the remaining whipped cream.
Run the tip of a knife around the edge of the cake. Cover with a clean sheet of parchment and a second baking sheet and invert the cake. Remove the first baking sheet and peel off the parchment. Brush the kirsch syrup evenly onto the cake to soak; reserve extra syrup for another use.
Using an offset spatula, spread the filling evenly on the cake. Scatter the cherries over the filling. Use the parchment to carefully roll the cake to form a 13-inch-long log with the seam on the bottom. Fold the parchment over the log so the ends meet. Using a ruler, squeeze the cake in the parchment to tighten the roll. Refrigerate for at least 1 hour.
Just before serving, whip the cream with the confectioners' sugar until firm. Transfer the cake to a serving platter and frost with the whipped cream. Sift the cocoa powder on top. Slice and serve.