In a bowl, whisk egg yolks with half of the sugar, salt, oil, coffee, and vanilla. Mix until smooth and slightly pale. This mixture forms the flavorful base of the sponge.
Sift the cake flour directly into the yolk mixture. Gently mix until just combined. Avoid overmixing or the cake may lose its softness.
In a clean bowl, beat egg whites with cream of tartar until foamy. Gradually add the remaining sugar and whip until soft peaks form. The whites should look glossy, not dry.
Fold one-third of the whipped egg whites into the yolk mixture to lighten it. Gently fold in the remaining whites until no streaks remain. Keep the motion light to preserve air.
Pour the batter into the prepared baking pan lined with parchment. Smooth the top and tap gently to release air bubbles. Bake until the surface springs back when lightly touched.
Whip the chilled cream with espresso powder and powdered sugar until firm peaks form. The cream should be smooth and spreadable, not stiff.
Once the cake cools slightly, peel off the parchment. Spread the coffee cream evenly across the surface. Roll the cake gently from one side and wrap it to hold shape. Chill before slicing.