Preheat the oven to 350 degrees Fahrenheit and lightly spray a 9×13 inch pan with non-stick cooking spray.
Combine the flour, baking powder, and salt in a large mixing bowl.
Using two separate bowls, separate the eggs. Placing the egg whites in one bowl and the egg yolks into the other bowl.
Add 3/4 cup of sugar to the bowl with the egg yolks and with an electric hand mixer, beat on high speed until yolks are pale yellow. Add the 1/3 cup whole milk and the vanilla and stir to combine.
Pour the egg yolk mixture over the flour mixture and stir gently just until combined.
With a handheld mixer or in the bowl of a stand mixer with the whisk attachment, beat the egg whites on high speed until soft peaks form (about 1 minute). With the mixer on medium-low, pour in remaining 1/4 cup sugar and then, beat on high speed until egg whites are stiff but not dry.
Gently, fold the egg whites into the batter, just until combined. Pour batter into prepared pan and spread the batter with a spatula to even out the surface.
Bake for 25 to 35 minutes, or until a toothpick inserted in the center of the cake comes out clean. Remove from the oven and allow the cake to cool completely.