Preheat the oven to 350 F. Spray two 8-inch round cake pans with cooking spray, line the bottoms with parchment paper, and set aside.
In the bowl of a stand mixer, beat ½ cup of butter on medium speed until creamy. Add in the granulated sugar, oil, and 1 tablespoon of vanilla extract. Continue beating until combined, stopping occasionally to scrape down the sides and the bottom of the bowl.
In a separate bowl, whisk together the flour, baking powder, and 1 teaspoon of salt.
With the stand mixer on medium speed, alternate adding the dry ingredients and 1 cup of milk into the bowl of the stand mixer, until everything is well-incorporated.
In another bowl, add the egg whites and use an electric mixer on high speed to beat them until stiff peaks form.
Gently fold the beaten egg whites into the cake batter until combined.
Divide the batter evenly between the two cake pans. Bake in the preheated oven for 35 to 40 minutes, until the cakes are golden and a toothpick inserted into the center of the cakes comes out clean.
Let the cakes cool for 15 minutes, then invert them onto a cooling rack and let them cool completely.
While the cakes are cooling, add the remaining 1 cup of butter to a large bowl. Beat on medium speed with an electric mixer until the butter is creamy. Add in the powdered sugar until combined, then add the remaining 1 tablespoon vanilla extract, ¼ teaspoon salt, and ¼ cup whole milk, and beat until the frosting is creamy.
Once the cakes are cool, spread ⅓ of the frosting evenly on top of one of the cakes. Add the second cake on top. Spread another ⅓ of the frosting evenly on top of the second cake, then spread the remaining frosting around the sides of the cake. Decorate as desired.
Refrigerate the cake until the frosting is set, then cut and serve.