Preheat oven to 350°F. Grease a 9x13-inch baking dish.
In a bowl, whisk together flour, baking powder, and salt.
In a separate bowl, beat egg yolks with ¾ cup sugar until pale, thick, and fluffy. Mix in milk and vanilla extract. Gently fold in the dry ingredients.
In another bowl, beat egg whites until soft peaks form. Gradually add the remaining ¼ cup sugar and beat to stiff, glossy peaks (not dry).
Gently fold the egg whites into the batter in batches, being careful not to deflate the mixture.
Pour batter into the prepared pan and spread evenly.
Bake for 22–25 minutes, until the top is lightly golden and the center springs back when touched. Let cool completely.