Start by heating your oven to 350°F (175°C). Take a baking sheet about 9 by 13 inches and line it with parchment paper, making sure it fits smoothly without any bubbles.
Separate the eggs into two bowls one for yolks, one for whites. Whisk the egg whites with a little salt until they form soft peaks, which means they hold their shape but aren’t stiff.
In another bowl, beat the egg yolks and sugar together until the mixture looks pale and fluffy. Add the vinegar, vanilla, and oil, and mix well.
Gently fold the beaten egg whites into the yolk mixture. Be careful so you don’t knock out the air you just whipped in.
Sift the flour and baking powder together in a separate bowl. Slowly add the dry ingredients into the wet mixture, alternating with the milk. Fold it all together gently until just combined, don’t overmix.
Pour the batter into your prepared baking sheet and spread it out evenly. Bake for about 12 minutes. The cake is ready when it springs back lightly when you press it.
Right after baking, flip the cake onto a kitchen towel dusted with powdered sugar. Peel off the parchment paper carefully. While the cake is still warm, roll it up in the towel from the short end and let it cool completely rolled up.
To make the filling, whip the heavy cream with sugar and vanilla until stiff peaks form. Beat the cream cheese until smooth, then fold it into the whipped cream gently.
Once the cake is cool, unroll it and spread the cream filling evenly on top. Sprinkle chopped berries over the cream. Roll the cake back up carefully and chill it for at least an hour before you slice and serve.