Preheat & Prepare Pans: Preheat your oven to 350°F (175°C). Grease your cake pans (see notes below for size) and dust with flour to prevent sticking.
Mix Dry Ingredients: In a separate medium-sized bowl, whisk together 528 g all purpose flour, 4½ teaspoon baking powder, and 1½ teaspoon salt. Set aside.
Cream Butter, Sugar & Oil: In the bowl of a stand mixer fitted with the paddle attachment, beat 112 g unsalted butter, softened on medium-high speed until creamy (about 2 minutes). Add 600 g granulated sugar and 1 cup vegetable oil, and continue beating until the mixture is light and fluffy. Scrape down the sides of the bowl as necessary. Mix in 4 teaspoons pure vanilla extract.
Combine Wet & Dry Ingredients: With the mixer running on medium speed, gradually add the the dry ingredients you had set aside and 1½ cups milk, alternating between the two, starting and ending with the flour mixture. Be sure to scrape the bowl occasionally to make sure everything is fully incorporated. Set aside.
Whip Egg Whites: In another clean bowl, beat 9 egg whites until stiff peaks form.
Fold in Egg Whites: Gently fold in the whipped egg whites, one-third at a time, using a spatula. Mix carefully so as not to deflate the whites—overmixing can result in a denser cake.
Bake the Cake: Evenly distribute the batter between your prepared pans. Bake for 35-40 minutes, or until a toothpick inserted in the center comes out clean.
Cool: Allow the cakes to cool in the pans for at least 20 minutes before flipping them onto a cooling rack. Let them cool completely before frosting.