Preheat the oven to 325°. Butter and flour two 9-inch-square cake pans.
In a medium bowl, whisk the cake flour, cocoa and baking powder. In a medium saucepan, melt the butter in the milk over low heat. Transfer to a large bowl and let cool slightly. Whisk in the egg yolks and 1/2 cup of the sugar. Add the dry ingredients and whisk until smooth.
In a clean bowl, beat the egg whites with the salt until soft peaks form. Gradually add the remaining 1/2 cup sugar and beat at medium-high speed until the whites are stiff and glossy. Fold the beaten whites into the batter until no streaks remain. Divide the batter between the pans and bake for 25 minutes, until the cakes are springy and a toothpick inserted in the centers comes out clean. Transfer the cakes to a rack and let cool completely.
Meanwhile, in a medium saucepan, bring the cream to a simmer. Put the chocolate in a heatproof bowl and pour the hot cream on top. Let stand for 3 minutes, then whisk until smooth. Let the frosting stand at room temperature, stirring occasionally, until thick enough to spread, about 1 hour.
Turn the cakes out of the pans and put one layer on a plate. Top with 1 cup of the frosting, spreading it to the edge. Top with the second layer and spread the remaining frosting over the top and sides. Let the cake stand at room temperature for about 30 minutes before cutting into squares.