Preheat the oven to 350°F (175°C). Line a 10x15 inch jelly roll pan with parchment paper.
In a bowl, whisk together flour, cocoa powder, baking powder, and salt.
In a separate large bowl, beat eggs with an electric mixer until thick and lemon-colored. Gradually add 1/2 cup of sugar and vanilla, beating well.
Gently fold the dry ingredients into the egg mixture until just combined. Spread evenly in the prepared pan.
Bake for 10 minutes. Immediately invert onto a clean kitchen towel dusted with confectioners' sugar, remove the parchment, and roll up in the towel. Let cool.
In another bowl, beat heavy cream with remaining sugar until soft peaks form. Carefully unroll the cake, spread the whipped cream, re-roll the cake without the towel, and refrigerate.