Preheat your oven to 180°C (350°F) and line a baking sheet with parchment paper, leaving enough overhang for easy lifting.
In a mixing bowl, beat the eggs and granulated sugar together with an electric mixer on high speed until pale and fluffy, about 5-7 minutes.
Sift together the all-purpose flour, cocoa powder, baking powder, and salt in a separate bowl.
Gently fold the dry ingredients into the egg mixture using a rubber spatula, being careful not to deflate the batter.
Drizzle the melted butter into the batter, and fold gently until just combined.
Pour the batter into the prepared baking sheet, spreading it evenly with an offset spatula.
Bake in the preheated oven for 10 minutes or until the cake springs back when lightly pressed.
Immediately turn the cake out onto a clean kitchen towel dusted with powdered sugar. Carefully peel off the parchment paper. Roll the cake tightly in the towel, starting from one short end. Let it cool completely for about 30 minutes.
While the cake cools, prepare the filling by whipping the heavy cream with the powdered sugar and vanilla extract until soft peaks form.
Once the cake is cool, unroll it carefully and spread the whipped cream evenly over the surface, using food coloring to create a marbled effect if desired.
Roll the cake back up without the towel, rolling from one short end to the other. Wrap it in plastic wrap and refrigerate for about 1 hour to set.
After chilling, remove the cake from the fridge and slice it into pieces, decorating with edible decorations like chocolate eggs or sprinkles for an Easter touch.