Preheat the oven to 350 degrees F (175 degrees C). Grease two 9 inch round cake pans. Dissolve the espresso powder and cocoa powder in the hot water; set aside to cool slightly.
In a large glass or metal bowl, whip egg whites to soft peaks. Gradually sprinkle in 1/4 cup sugar while continuing to whip until stiff, but not dry.
In a separate bowl, whip egg yolks with remaining sugar until thick and pale, about 5 minutes. Stir in the espresso mixture, then sift in the flour, baking powder and salt. Gently stir until incorporated. Fold 1/3 of the egg whites into the batter until very well mixed, then gently fold in the remaining egg whites. A few streaks are okay. Divide the batter between the two prepared pans, and spread evenly.
Bake for 25 to 30 minutes in the preheated oven, until the top of the cake springs back when lightly pressed.
