Preheat the oven to 350 degrees F. Grease a 9x13 inch baking pan.
Separate Eggs. To start, separate the egg yolks and whites. Place the yolks in a large bowl. Place the whites in a separate large bowl. Make sure there are NO bits of yolk in the egg whites. (Even a tiny drop can prevent them from whipping properly.)
Combine Dry Ingredients. In a small bowl, whisk together gluten-free flour, baking powder, and salt to combine. Set aside.
Combine Egg Yolks & Sugar. Add 3/4 cup sugar to the egg yolks. Stir until smooth. Mix in the vanilla and whole milk.
Whip Egg Whites. Use a hand mixer to blend the eggs until foamy and starting to turn white. Gradually add in the last 1/4 cup sugar and whip until the egg white turn into stiff peaks. (When you lift the beaters out of the mixture, it should hold its shape on the beaters even when you rotate them around.)
Mix Cake Batter. Add dry ingredients to the egg yolk mixture and stir until just combined. Add about half of the whipped egg whites mixture to the batter and use a spatula to gently fold it into the batter. (Don't stir or you'll deflate it. Instead, scrape around the edges of the bowl and fold it in on top of itself in the center.) Add the second half of the whites mixture and repeat.
Bake Cake. Pour batter into the prepared baking pan. Bake at 350 degrees 28-30 minutes, or until the top is golden and a toothpick inserted in the center of the cake comes out clean with just a few moist crumbs (no wet batter). Let the cake cool to room temperature while you prepare the milk mixture. (It may settle a bit while it cools--this is normal!)