Preheat the oven to 350℉ and grease a 9x13" pan.
In a bowl, whisk together the flour, baking powder, and salt.
1 cup all-purpose flour, 1 ½ teaspoons baking powder, ¼ teaspoon kosher salt
In two separate bowls, separate the egg yolks from the whites, being sure not to let any yolks get into the whites or else they won't whip properly.
Add the egg whites to a stand mixer bowl with the whisk attachment and whip on high speed until soft peaks begin to form. Gradually add ¼ cup (50g) sugar and continue to whip until stiff peaks form.
Transfer the egg whites to another bowl, scraping out as much as possible (no need to wash it).
Add ¾ cup (150g) sugar and the egg yolks to stand mixer bowl and beat on medium high speed (using the paddle attachment) until the yolks are pale yellow (about 3-4 minutes).
Scrape down the sides, then add the ⅓ cup milk (80ml) and vanilla and mix on low to combine.
Add the flour mixture to the whipped yolks and fold it together until smooth.
Fold the egg whites into the batter in two batches until just combined, careful not to stir and deflate the batter.
Pour the batter into the prepared pan and smooth it evenly with a spatula. Bake the cake for 25-30 minutes until completely set. The cake will have pulled away from the edges of the pan and be slightly browned. Allow the cake to cool slightly on a wire rack.