For the cake:
Preheat the oven to 350°F. Butter or oil a 10-by-15-inch jellyroll pan or a 16-3/4 by 12-inch sheet pan. Line the bottom lengthwise with a piece of waxed or parchment paper.
Combine the chocolate and coffee in a heat-safe bowl and microwave for 45 seconds. Stir, and continue to heat in 20-second bursts, until the chocolate is almost melted. Continue to stir until melted completely. Let cool.
In the bowl of an electric mixer fitted with the paddle attachment, beat the egg yolks until pale and creamy. Gradually add the sugar and continue to beat until yolks are pale and ribbony. Gently stir the cooled chocolate into the yolk mixture.
In a clean bowl of an electric mixer fitted with the whisk attachment, beat egg whites with salt until they hold stiff peaks. Stir a quarter of egg white mixture into the chocolate-yolk mixture to lighten it. Gently fold the remaining whites into the cake batter in three additions. Pour the batter into the prepared pan and smooth top. Bake in preheated oven for 15 minutes for a jelly roll pan and 12 minutes for a half sheet pan, or until cake layer feels dry (but very soft) to the touch and a toothpick inserted into the center comes out clean. It will still seem a little underbaked.
Transfer to a cooling rack and cover the top with a lightly damp towel for 10 minutes.Remove towels and run a knife around the edges of the cake. Sift one tablespoon of cocoa over the top of the cake and cover the cake with a thin tea or flour sack towel that is a little longer than the pan. Place the back of a baking sheet or a large flat tray over the towel and invert the cake onto it. Gently peel back the parchment paper. Sift the remaining tablespoon of cocoa powder over the top of the cake. Roll the cake up with the towel from short end to short end so the towel is inside. Let cool completely, seam side down.
For the filling:
Once cool, beat heavy cream with powdered sugar and vanilla until it holds stiff peaks. Get your serving plate ready and place it near your cake roll. Gently unroll the chocolate cake. Spread the whipped cream filling evenly over cake, leaving a 1-inch border at the far edge. Gently use the tea towel once again to reroll cake and place on the serving plate. Wrap the log tightly in plastic to keep its shape and store in the fridge while preparing the ganache.
For the ganache:
In glass measuring cup, microwave the chocolate and cream for 45 seconds. Stir and continue to heat in 20-second bursts until melted and smooth. Chill until thickened, about 10 minutes.
Remove the plastic from the cake and trim both end pieces. Spoon the ganache over the cake and smooth over the sides. Chill for 1 hour, or until set, before slicing and serving.
The cake can be stored in an airtight container in the fridge for up to 2 days, though the filling will deflate the longer it’s stored.