Preheat the oven to 175°C. Grease and line a 33 x 23cm Swiss roll tin and set aside.
Place the eggs into the bowl of a stand mixer (or use an electric whisk) and whip on high speed until frothy and doubled in volume. Add the sugar, one tbsp at a time, with the mixer going, until it has all been incorporated. Beat the mixture for a further 5-8 minutes until tripled in volume and has reached the 'ribbon stage'.
Whisk the oil, milk, vinegar and vanilla extract together in a small jug. With the mixer on low, slowly pour the wet ingredients into the egg mixture.
Sift the flour, baking powder and salt into the mixture, then fold in using a large, metal spoon, until no streaks of flour remain.
Pour the batter into the prepared tin and gently level the top. Bake in the preheated oven for 12-14 minutes, until golden and just about springs back when touched gently. Be careful not to over-bake the cake, or it will be harder to roll without cracking.
While the cake is baking, spread a piece of baking paper larger than the size of the Swiss Roll tin on the work surface and sprinkle it with the 2 tbsp caster sugar.
When the cake comes out of the oven, leave it to stand for 1 minute, then tip it out onto the sugared baking paper. Carefully peel off the baking paper from the surface of the cake, then use the new baking paper to help you roll the cake up quite tightly. Leave the cake to cool completely in this roll before filling/decorating.