Prepare pans: Preheat oven to 350°F (175°C). Line two 8-inch round cake pans with parchment paper and generously grease and flour the sides. Shake out excess flour.

Cream butter mixture: In a stand mixer bowl, beat softened butter on medium-low speed until creamy. Add sugar and oil, beating until well-combined and fluffy.

Add vanilla: Scrape down sides and bottom of bowl, then stir in vanilla extract until combined.

Combine dry ingredients: In a separate bowl, whisk together flour, baking powder, and salt until evenly distributed.

Alternate wet and dry: With mixer on medium speed, gradually alternate adding flour mixture and milk to butter mixture, starting and ending with flour. Mix until each addition is almost completely combined before adding the next.

Whip egg whites: In a completely clean bowl, beat egg whites with hand mixer on high speed until stiff peaks form (several minutes). Peaks should hold their shape when beater is lifted.

Fold gently: Using a rubber spatula, gently fold whipped egg whites into cake batter. Fold carefully to avoid deflating the whites while ensuring they're well incorporated.

Bake: Divide batter evenly between prepared pans. Bake for 35-40 minutes, rotating pans halfway through, until toothpick inserted in center comes out clean or with few moist crumbs.

Cool: Remove from oven and cool in pans for 15 minutes. Run knife around edges, then invert onto wire racks. Cool completely before frosting.