Preheat oven to 375. Grease two 9x2 inch round cake pans and line the bottoms with rounds parchment or wax paper. Grease paper and dust insides of pans with flour.
Using the whisk attachment of a stand mixer, beat yolks at high speed for about 5 min until light. Add half of the sugar and beat another 5 minutes until very thick and mixture forms a wide ribbon when the beaters are lifted. Add cocoa and beat until blended, scraping sides of bowl.
In a large metal or glass bowl and using a handheld electric mixer, beat the egg whites and salt until egg whites hold soft peaks. Very gradually add the remaining sugar. In small additions, fold about half of the whites into the chocolate mixture, then fold the chocolate mixture into the remaining whites. Turn into pans and smooth each layer. If you have a scale and want to make sure the batter is evenly divided, weigh a little over 8 ounces of batter into each pan.
Bake in lower third of oven for 30 min. until layers spring back when pressed with fingertip and begin to come away from sides of pan. Loosen warm cakes with a knife, then remove layers from pan, remove paper, and invert again to let layers cool right side up. They will buckle and sink and be uneven, but that's to be expected.
Place 4 10x3 inch pieces of wax paper or parchment around edges of cake plate and place the first layer of cake upside down so that it touches the paper pieces, but the paper pieces are still sticking out from under the cake.
Filling: Sprinkle gelatin over water in small cup and let stand for 5 min, then set the cup in skillet you've filled with about an inch of hot water. This helps dissolve the gelatin. Remove cup from hot water and set aside.
Set aside 3 tablespoons of the cold cream and put the rest in a clean mixing bowl. Add sugar and vanilla to the cream in the mixing bowl and whip only until it holds a soft shape. Quickly stir remaining cream into the dissolved gelatin and pour into the softly whipped cream. Continue whipping until cream holds a firm shape. Cover bottom layer of cake with cream and cap with top layer. Refrigerate while preparing icing.
Icing: Place chopped chocolate and butter and coffee (which has been dissolved in boiling water) in a saucepan over very low heat. Stir occasionally until melted and remove from heat. Alternatively, you can melt this in a microwave-safe bowl and heat at 50% power, stirring every 30 seconds, until smooth. Cool just to room temperature.
Beat cream, powdered sugar and vanilla together just until mixture thickens a bit and holds a soft shape. THIS IS IMPORTANT. If you overdo it here, the icing will be too stiff and will have a slightly curdled appearance. Fold half the cream gradually into the chocolate mixture, then fold that into the remaining cream. Use as much of the icing as you need to fill in any hollows on the sides of the cake and then smooth icing all over. Pull away the parchment paper pieces the cake is sitting on.
Refrigerate at least 6 hours or overnight and serve cold. To slice without squashing cake, insert the point of a sharp knife in the center of the cake, then cut with an up-and-down sawing motion.