Begin with the buttercream filling. In a mixer, combine powdered sugar, butter, liqueur, cocoa powder, and salt. Once blended, fold in the mascarpone cheese and set aside.
Preheat the oven to 400°F (200°C). Brush a 13x18-inch pan with melted butter, line with parchment paper, and brush again.
In a bowl, sift together cocoa powder, flour, and salt.
In a separate bowl, whip eggs and sugar until fluffy. Gradually add vanilla and the cocoa mixture, blending until just combined.
Spread the batter onto the prepared pan and bake for 8-10 minutes.
Once baked, invert the cake onto a sugar-dusted kitchen towel. Remove the parchment paper, dust with more sugar, and gently roll the cake. Let it cool for 15 minutes.
Unroll the cooled cake, spread the buttercream filling, and re-roll. Dust with powdered sugar and refrigerate for 2 hours.
For the ganache, pour hot cream over chocolate chips, let sit for a minute, then whisk until smooth. Frost the log and create bark-like ridges with a knife. Chill before serving.