Preheat your oven to 375°F (190°C) and line a 15x10-inch baking sheet with parchment paper.
In a large mixing bowl, beat the eggs and sugar with an electric mixer on high until the mixture is thick, pale, and tripled in volume—about 5 minutes. You’ll notice it becoming fluffy and almost ribbon-like.
Sift together the flour and cocoa powder, then gently fold them into the egg mixture using a spatula, trying to maintain as much air as possible for a light sponge.
Pour in the melted butter and vanilla extract, folding gently until just combined. The batter should be smooth and shiny.
Pour the batter into the prepared baking sheet, spreading it evenly to the edges with a spatula. Tap the pan lightly on the counter to remove any air bubbles.
Bake for 12-15 minutes, or until the sponge is set but still slightly springy when pressed. The aroma of cocoa will fill your kitchen as it bakes.
Once baked, invert the sheet onto a clean kitchen towel dusted lightly with cocoa powder, then gently peel off the parchment paper. Let the sponge cool completely while you prepare the filling.
In a mixing bowl, whip the heavy cream, powdered sugar, and cocoa powder until stiff peaks form—the cream should be smooth, fluffy, and slightly glossy.
Spread the chocolate whipped cream evenly over the cooled sponge, leaving a small border around the edges.
Carefully roll up the sponge from one short end to the other, using the towel to help lift and guide the roll without cracking the sponge. Aim for a tight, even spiral.
Place the rolled cake seam-side down on a serving plate, and chill for at least 30 minutes to set before slicing and serving.