Preheat the oven to 350°F (175°C). Line a 10×15 inch jelly roll pan with parchment paper and lightly grease it.
In a large bowl, beat the egg yolks with 1/2 cup granulated sugar until the mixture is thick, pale, and forms ribbons when lifted, about 3-4 minutes. Stir in 1/2 teaspoon vanilla extract.
In a separate bowl, sift together the cocoa powder, flour, and salt.
Gently fold the dry ingredients into the egg yolk mixture until just combined.
In a clean bowl, beat the egg whites with cream of tartar until soft peaks form. Gradually add the remaining 1/4 cup granulated sugar and continue beating until stiff peaks form.
Carefully fold the beaten egg whites into the chocolate batter in three additions, ensuring not to deflate the mixture.
Pour the batter evenly into the prepared pan and spread gently to the edges.
Bake for 10-12 minutes, or until the cake springs back lightly when touched and a toothpick inserted in the center comes out clean.
While the cake bakes, lay a clean kitchen towel on a flat surface and dust it generously with powdered sugar.
Once baked, immediately invert the cake onto the prepared towel and carefully peel off the parchment paper.
Starting from the short edge, roll the cake and towel together into a tight spiral. Allow to cool completely in this rolled shape.
To prepare the filling, whip the heavy cream with powdered sugar and 1/2 teaspoon vanilla extract until stiff peaks form.
Unroll the cooled cake gently and spread the whipped cream evenly over the surface.
Roll the cake back up without the towel, wrap in plastic wrap, and refrigerate for at least 1 hour before serving.
Slice and serve chilled.