Preheat oven to 350°F (175°C) and grease a 9×13-inch baking pan.
In a medium bowl, whisk together flour, baking powder, and salt.
In a large bowl, beat egg yolks with ½ cup sugar until thick and pale.
Mix in milk, vanilla, and oil until smooth.
Gently fold in the dry ingredients until just combined.
In a separate bowl, beat egg whites to soft peaks. Add remaining sugar and beat to stiff peaks.
Fold the egg whites into the batter in 2–3 additions, keeping the batter light and airy.
Pour into prepared pan and bake for 26–28 minutes, until set.
Let cake cool completely.