Preheat oven to 350F. Grease a 10x15" pan and line with parchment paper. Set aside.
In a large bowl beat together the egg yolks, vanilla paste, milk and sugar on high speed until thick 8-10 minutes. Then pour in the vegetable oil and whisk that in. Sift in the cake flour, baking powder, salt, and espresso powder and give it another good whisk until everything is combined.
In a separate bowl, whisk egg whites with cream of tartar on low speed until foamy. Gradually add the sugar, a tablespoon at a time, until you reach stiff peaks.
Add the egg white mixture to the egg yolk mixture and gently fold until well blended. The batter should be light and airy.
Pour the batter into your prepared pan. Gently tap on your counter a few times to release air bubbles.
Bake for 15 minutes or until the cake springs back when gently pressed or a toothpick inserted in the center comes out clean.
While the cake is still warm, run a knife around the edges of the pan, place a clean tea towel on top, and carefully invert the cake. Remove the pan and peel off the parchment paper.
Carefully roll the cake, do not roll too tight or it might crack. Allow the cake to cool completely before frosting.