Heat the oven to 350°F, grease a 9-inch round pan, and line its base with parchment.
Whisk flour, baking powder, and salt. Beat eggs and sugar until thick and pale, then fold in the dry ingredients, warm milk, and vanilla.
Bake 25 to 30 minutes, until the center springs back. Cool completely and split the cake horizontally.
For pastry cream, heat milk until steaming. Whisk sugar, yolks, and cornstarch, slowly whisk in hot milk, then cook until thick. Stir in butter, cover the surface, and chill.
Spread chilled pastry cream over the bottom cake layer and replace the top layer.
Heat cream until steaming, pour over chocolate, rest two minutes, and stir smooth. Spread the ganache over the cake and chill until set.