Preheat oven: Set your oven to 350°F. Line a 13 x 18-inch baking pan with parchment paper, then spray it lightly with nonstick cooking spray to prevent sticking.
Mix yolks: In a large bowl, beat together the separated egg yolks, sugar, melted butter, and vanilla until creamy and smooth. Then, mix in the espresso powder and cocoa until fully combined.
Whip egg whites: In a separate bowl, whip the egg whites until stiff peaks form.
Combine dry ingredients: In another bowl, combine the flour, baking powder, and salt. Gradually stir this mixture into the chocolate-yolk mixture until just incorporated.
Fold in egg whites: Gently fold the whipped egg whites into the batter.
Spread batter: Pour the batter into the prepared baking pan and spread it evenly.
Bake cake: Bake in the preheated oven for about 10 minutes or until a toothpick inserted in the center comes out clean.
Roll the cake: Once out of the oven, immediately roll the warm cake up, starting at one small end.
Cool on a rack: Transfer the rolled cake to a wire rack and let it cool completely.
Prepare filling: In a bowl, beat the mascarpone cheese, granulated sugar, and coffee liqueur until smooth.
Whip cream: In a separate bowl, whip the heavy cream until stiff peaks form. Gently fold this into the mascarpone mixture.
Spread filling: Unroll the cooled cake and spread two-thirds of the mascarpone mixture evenly over the surface.
Re-roll the cake: Carefully roll the cake back up, enclosing the creamy filling.
Finish it off: Spread the remaining mascarpone mixture over the top of the cake. Dust with cocoa powder and garnish with shaved chocolate.