Preheat oven to 350 degrees. Line a 20” x 15” rimmed baking sheet with parchment paper. Coat parchment with nonstick spray or butter.
Stir together flour, ½ cup cocoa, baking powder, and salt in a bowl with a wire whisk.
In a stand mixer with whisk attachment, beat eggs, sugar, and coffee until light and fluffy. Carefully add melted butter and beat until just combined. At low speed, add dry ingredients to egg mixture in 1⁄2-cup increments until just combined and streak-free. Do not overmix.
Spread batter evenly in prepared pan and bake 12 to 14 minutes, or until it just springs back to the touch. Do not overbake.
Remove cake from oven and allow to cool in pan for 8 to 10 minutes. Spread a clean dishtowel on the counter. Sift the remaining 1 tablespoon cocoa in an even, very light coating on the surface of the cake using a sieve. Use a small knife to make sure that the margins of the cake are free of the pan and parchment, then quickly invert pan onto towel. Carefully peel back the parchment.
Starting on the long side, gently and slowly roll the cake into the towel. Place on a wire rack, cake seam down. Allow to cool completely thus, while you make the filling and frosting (recipes below).
To fill, unroll cake, and spread cooled ganache filling evenly over. Re-roll (excluding towel), wrap airtight, and chill for two hours.
Halve or trim chilled cake to suit your serving platter(s). Place cake on wire rack. Drizzle tepid ganache frosting over cake, using about ⅔ of the mixture. Spread the frosting for complete coverage.
As the unused ganache frosting continues to cool, it will thicken further. After about 30 minutes, you should be able to apply and trowel it to achieve a bark-like textured effect.
Plate cakes, dust with powdered sugar, or otherwise decorate to your heart’s content, and serve.