Prep the pans: Preheat the oven to 350 degrees F. Fold a large sheet of parchment paper in half; put a 10-inch-round cake pan on top. Trace the cake pan, then cut out the circle to make two rounds of parchment. Spray two 10-inch cake pans with cooking spray; fit a parchment round into each. Spray the pans again, then dust with flour and tap out the excess.
Make the batter: Pour the coffee into a liquid measuring cup or bowl; whisk in the cocoa powder. Put the flour, salt, baking soda, baking powder and sugar in the bowl of a stand mixer; mix with the paddle attachment on low speed, 1 minute. Add the eggs, vegetable oil, vanilla and 2 cups water; beat on medium speed, 2 minutes. Reduce the speed to low; beat in the coffee-cocoa mixture in a slow stream until combined. The batter will be thin.
Bake the cakes: Divide the batter between the prepared pans. Bake until a skewer inserted into the middle comes out clean, 50 minutes to 1 hour. Let cool in the pans on a rack, 10 minutes, then turn the cakes out onto the rack to cool completely. Place each cake on a 10-inch cardboard cake circle (this helps stabilize the layers as you move them around), wrap in plastic wrap and refrigerate at least 4 hours or overnight.
Make the ganache: Pulverize the bittersweet chocolate in a large food processor. Bring the cream just to a boil. With the motor running, pour the hot cream through the feed tube; process until smooth. Transfer to a large bowl and set in a bowl of ice water. Chill, stirring often, until the ganache is cool but not stiff, about 20 minutes.
Make the bark: Microwave the white chocolate in 15-second intervals until two-thirds melted; stir to fully melt. Scrape into a zip-top bag and seal. Put a plastic sheet protector on each of 2 baking sheets. Snip a corner of the bag; pipe thin lines of white chocolate over the sheets.
Refrigerate the baking sheets until the white chocolate is set, about 10 minutes, then repeat the process with the milk chocolate, piping thin lines over the white chocolate. Refrigerate until the milk chocolate is set.
Melt the bittersweet chocolate in the same way, then spread over the white and milk chocolate lines using an offset spatula. Refrigerate until hard, about 30 minutes.
Peel the sheet protectors off the chocolate and break the chocolate sheets into shards of various sizes.
Slice the layers: Put one cake on a cake turntable. Position a long serrated knife against the side of the cake, about halfway down. Slowly rotate the turntable so the knife slices the cake in half horizontally. Don't move the knife much-let the rotation of the turntable do the work. Repeat with the other cake to make 4 layers; transfer each to a cardboard circle. (If you don't have a turntable, carefully slice the cakes in half on a cutting board.)
Frost the cake: Transfer half of the ganache to a bowl and whisk until light brown and fluffy. Place one cake layer (still on a cardboard circle) on the turntable; spoon one-third of the whipped ganache on top. Rotate the turntable to smooth the ganache with a long spatula (or just assemble and frost on a cake plate). Repeat to sandwich all 4 cake layers with whipped ganache. Spread all but about 1/2 cup of the unwhipped ganache over the top and sides of the cake.
Decorate the cake: Press the chocolate bark against the sides of the cake, using small dollops of the remaining ganache to help the pieces stick, if necessary.
Photograph by Pernille Pedersen
Recipe courtesy Ron Ben-Israel for Food Network Magazine