Preheat the oven to 180°C (350°F) and line a baking tray with parchment paper.
In a mixing bowl, whisk together eggs and sugar until the mixture is pale and fluffy.
Sift together flour, cocoa powder, baking powder, and salt in a separate bowl.
Gradually fold the dry mixture into the egg mixture, being careful not to deflate the batter.
Gently mix in the cooled brewed coffee until just combined.
Pour the batter into the prepared baking tray and spread it evenly.
Bake for 10-12 minutes until the cake springs back when touched lightly.
While the cake bakes, prepare a clean kitchen towel dusted with powdered sugar.
Once baked, immediately turn the cake onto the prepared towel and peel off the parchment paper.
Starting from one edge, gently roll the cake with the towel to form a log shape.
Meanwhile, whip the heavy cream with powdered sugar and vanilla extract until soft peaks form.
Unroll the cooled cake and spread the whipped cream evenly over the surface.
Re-roll the cake without the towel, creating a spiral effect with the filling inside.
Wrap the Swiss roll in plastic wrap and refrigerate for at least 1 hour before serving.
Before serving, garnish with chocolate shavings for a decorative finish.