Step 1: Preheat your oven to 350°F (175°C) and line a 10×15 inch jelly roll pan with parchment paper, greasing the paper slightly.
Step 2: In a large bowl, whisk the egg yolks with 1/4 cup of sugar until pale and thickened. Stir in the cooled espresso and vanilla extract.
Step 3: Sift together the cake flour, cocoa powder, baking powder, and salt. Gradually fold the dry ingredients into the egg yolk mixture until just combined.
Step 4: In a separate clean bowl, beat the egg whites until soft peaks form. Gradually add the remaining 1/4 cup of sugar and continue beating until stiff, glossy peaks form.
Step 5: Gently fold one-third of the egg whites into the chocolate batter to lighten it, then fold in the remaining whites carefully to maintain volume.
Step 6: Spread the batter evenly into the prepared pan and bake for 10-12 minutes or until the cake springs back when touched.
Step 7: Immediately invert the hot cake onto a kitchen towel dusted with cocoa powder. Peel off the parchment and roll the cake and towel together from the short end. Let cool completely.
Step 8: Whip the heavy cream with powdered sugar and espresso powder until stiff peaks form. Unroll the cooled cake, spread the cream, and re-roll. Chill for 2 hours before serving.