Preheat oven to 350°F.
Grease and line a 12×17-inch baking sheet with parchment, then grease the paper.
Beat egg whites with ¼ cup sugar until stiff peaks form (about 5 minutes).
In another bowl, beat egg yolks, ½ cup sugar, oil, vanilla, and salt until fluffy.
Sift flour, cocoa powder, and baking powder into the yolk mixture; mix on low speed.
Fold egg whites into the yolk mixture in three additions until fully combined.
Spread batter into the prepared pan and bake for 12–15 minutes, or until the cake springs back when pressed.
Lay a clean kitchen towel on the counter and dust it generously with cocoa powder.
Immediately after baking, loosen the cake edges, flip it onto the towel, peel off the parchment, and roll the cake up in the towel from the short end.
Let cool for 2 hours.
Beat heavy cream with sugar and vanilla until stiff peaks form.
Unroll the cooled cake, spread the whipped cream evenly, then gently roll it back up using the towel to assist.
Place the roll seam-side down on a wire rack.
Heat cream until steaming and pour over chocolate in a bowl and let sit for 10 minutes.
Stir in oil until smooth.
Pour ganache over the roll, spread to coat, and let set for 30 minutes before slicing or chilling.