Grease and flour two 9-inch round cake pans. If desired, line the pans with greased and floured waxed paper.
Separate the eggs. Lightly beat the yolks and set them aside. Beat the whites until stiff peaks form. Set the whites aside.
Combine in the top of a double boiler the baking chocolate, 4 tablespoons of sugar and 2 tablespoons of milk. Stir together over hot water until chocolate is completely melted.
In a large mixing bowl, cream the butter. Add the rest of the sugar, the beaten egg yolks, and the melted chocolate mixture. Stir well.
Sift together the dry ingredients and add them to the batter, alternating with the rest of the milk. Fold in the stiffly beaten egg whites and the vanilla.
Pour the batter into the prepared pans. Bake for 20 minutes or until the layers begin to pull away from the sides of the pans. Check for doneness with a cake tester. Take care not to over bake so the layers do not become dry.
Remove pans from the oven and place on racks to cool for 10 minutes.
Remove the layers from the pans (peel off the waxed paper if you used it) and finish cooling completely on the racks.
Frost when the layers are completely cool.
Make the frosting:
Sift the powdered sugar and cocoa into a medium-size mixing bowl.
Add the melted butter and enough coffee to make a good spreading consistency.
Beat well with a wire whisk or electric mixer.
Stir in the vanilla.
Spread frosting on cooled cake layers.
A note about the frosting: if it seems too thin, just add more confectioner's sugar a few tablespoons at a time until you get the right consistency. Sometimes it's fine, other times it's just too runny for me. Maybe it's the weather, I'm not sure. However, the additional confectioner's sugar will correct it every time